HN Theater @HNTheaterMonth

⬐ vmilner

I love this so much - I’ve been trying to encourage anyone starting a linear algebra course to watch this - LA cries out for this type of visualisation help.

Two quick things I can recommend without hesitation, which focus on an intuitive understanding of concepts:

1. Essence of Linear Algebra mini-series - https://m.youtube.com/watch?v=kjBOesZCoqc

2. Better Explained website - https://betterexplained.com

YouTube has a lot of high quality math content, it definitely helped through university. It's also worth mentioning the Stanford U courses.

The main takeaway I have for you is learn the concepts intuitively first, then spend the time to play around with them on paper until they sink in. Some things will be easy, some will be frustrating, much like programming you will walk away from a frustrating problem and have an epiphany while doing something completely different.

All the best and have fun!

⬐ Entalpi

My two cents are whenever something seems hard/impossible/infuriating/etc, take a break then seek dofferent sources on the material. A lot of times I have been hung up on something only to find that things make much more sense when approaching it from a different viewpoint. :)

⬐ dvddgld

Absolutely! Not having to hit your head against a wall helps prevent burnout as well as just plain being more effective

⬐ chris_wot

That’s how I got to grips with trigonometry... I tried to understand why sine, cosine, tangent, cotangent, secant and close can’t we’re named like they were... then I found a bunch of stuff on the unit circle. Never looked back!

⬐ Bizarro

No matter what I'm learning, I always refer to at least 3 different sources for any concept.

+1

And definitely follow through his "pause and ponder" sections. If you want to build up your maths skills, it is crucial to learn how to think in the maths way. Like becoming a good programmer involves writing lots of code yourself, or to become a good dancer you need to practice your steps. For maths it's abstract thinking. Appreciation of maths is one thing, having the discipline to self-study a whole other.

Edit. Regarding your 2nd Edit: His videos are made for the broadest audience possible. I'd recommend picking any video whose topic interests you the most at the moment. You will see what knowledge you lack (take notes of these!) and can expand from there. Be it to watch his maths fundamental ((1)) series [0],[1] or just rewatch.

((1)): As in any other things, knowing your fundamentals is significant to the understanding of a topic. It won't help you at all if you can apply (copy paste) some machine learning techniques if you don't know about linear algebra at all.

[0]: https://www.youtube.com/watch?v=kjBOesZCoqc&list=PLZHQObOWTQ...

[1]: https://www.youtube.com/watch?v=WUvTyaaNkzM&list=PLZHQObOWTQ...

I'll always recommend 3blue1brown's incomparable videos on linear algebra: https://www.youtube.com/watch?v=kjBOesZCoqc&list=PLZHQObOWTQ...

⬐ 0x4FFC8F

The best, hands down on YouTube.

For an article like this I find that static visualizations aren't anywhere near as effective as dynamic ones found in a similar explanation here (3Blue1Brown on Linear Algebra Transformations)

https://www.youtube.com/watch?v=kjBOesZCoqc&list=PLZHQObOWTQ...

So many things I could say about this, but I"ll let Alan Kay speak for me - https://youtu.be/p2LZLYcu_JY Alan talks about how ideas in Calculus could be manifested from an early age and a richness in understanding built up as they aged up:

- at very young ages, kids really respond well through "doing" / the enactive channel. When asked to draw a circle, kids in Papert's group would first emulate what a LOGO turtle would do by rotating their body in a circle (making tiny increments in x and y).

- as they got a bit older, the visual / iconic channel was more developed and they could understand the abstraction of a circle on pencil/paper and how the concepts carried over there

- closer to early teens, symbols were much easier to grasp and relate to, etc.

With this context in mind, there have been some cool efforts to mix the second and third channels I just mentioned to communicate advanced math concepts. Vi Hart and Grant Sanderson's youtube channels come to mind. Here are my favorite videos by Grant:

- "What does it feel like to invent math": https://www.youtube.com/watch?v=XFDM1ip5HdU

- On the visual intuition behind a hard problem on the Putnam exam - "The hardest problem on the hardest test": https://www.youtube.com/watch?v=OkmNXy7er84

- From vectors to matrices to vector spaces to higher-level ideas like the link between linear algebra and calculus: "Essence of linear algebra" series: https://www.youtube.com/watch?v=kjBOesZCoqc&list=PLZHQObOWTQ...

What I especially like about Grant's videos, is that he often walks through what a mathematician would do, the questions she would ask, etc.

If anyone's looking for a (high level) overview of linear algebra, I'd highly recommend 3blue1brown's video series: https://www.youtube.com/watch?v=kjBOesZCoqc&list=PLZHQObOWTQ...

It's mostly graphical, and is really helpful in forming and cementing an intuition for linear algebra.

⬐ Izkata

Ran across these videos a few months ago; at one video a night (~15-20 minutes a day over two weeks), it gave me a better intuitive understanding of linear algebra than a full semester in college. These videos should be required before diving into the math in class, I'd've definitely done better had I seen these beforehand.

⬐ InclinedPlane

I really hate the way that mathematics is taught in most school systems, it's all machinery with none of the beauty and underlying understanding. I was lucky enough to maintain an interest in mathematics sufficient to allow me to basically teach myself, with a heavy reliance on an underlying conceptual understanding. A lot of things like calculus and linear algebra are mostly just about understanding the basic concepts and then building up some experience working with them. There's no need to memorize gazillions of formulae or anything like that, you just need to actually know what you're doing when you do the work, but you will inevitably rely on tables and references except for very simple work.

Which is to say, I could not recommend 3blue1brown's videos more highly, they are an invaluable aid to learning linear algebra and actually helping you understand what is you're doing when you're doing these various operations to "solve problems".

For linear algebra basics, I also especially recommend 3Blue1Brown's youtube channel and his "Essence of" series:

https://www.youtube.com/watch?v=kjBOesZCoqc&list=PLZHQObOWTQ...

I've never seen the material presented more clearly - it's completely visual and focused on building intuition first.

Is there any book which actually explains where matrix and its rules come from? Instead of throwing on you matrix multiplication rules in dogmatic way so you blindly follow them like mindless robot?

I know there are lectures in YouTube from 3Blue1Brown:

https://www.youtube.com/watch?v=kjBOesZCoqc&list=PLZHQObOWTQ...

So I want a book which covers linear algebra in the similar manner.

⬐ dmit

http://linear.axler.net/

⬐ hexrcs

I second this. Linear Algebra Done Right is an awesome book. It also comes with a helpful selection of exercises after each chapter with detailed answers available on the website, which is great for self-learners. If you are a student and your Uni has a Springer subscription, you might be able to get the PDF for free.

⬐ jasode

"Linear Algebra Done Right" is a fine book but its enduring popularity leads people to recommend it as a universal default answer.

The parent asked if there was a LA book that covered the material in the same style as 3Blue1Brown's videos. If that's the criteria, Sheldon Axler's book isn't the best book. One can compare a sample chapter to the youtube videos and realize they use different pedagogy:

http://linear.axler.net/Eigenvalues.pdf

⬐ ivan_ah

For intuition about linearity, check out this intro jupyter notebook: https://github.com/minireference/noBSLAnotebooks/blob/master... and the associated video https://www.youtube.com/watch?v=WfrwVMTgrfc

⬐ fnl

The No Bullshit Guide to Linear Algebra https://gumroad.com/l/noBSLA#

⬐ keithpeter

I like the look of the presentation and the active teaching method adopted. I also like the way Savov gives out the definitions and the facts as a pdf but keeps the exercises, investigations and examples for the paid version - the exercises are the value added in Maths in my limited experience.

I just bought the paper version off Lulu (I like being able to read and scribble and then go on the computer for the computational exercises). And now to set up SymPy on Debian...

⬐ foota

There was a web book I found a while ago that built up some sort of motivation for linear algebra. Unfortunately I don't remember what it was or the title.

Edit: found it, https://graphicallinearalgebra.net

Ymmv. Matrix multiplication is defined the way it is imo because it has interesting properties that way. Not very satisfying though.

⬐ dragandj

You might find my Clojure Linear Algebra Refresher helpful.

http://dragan.rocks/articles/17/Clojure-Linear-Algebra-Refre...

This is the link for the first part. You'll find further articles there.

It walks you through the code, explain things briefly, and points you to the exact places in a good Linear Algebra with Application textbook where this is explained in detail.

⬐ jtmcmc

my linear algebra teacher taught it in a visual and proof focused way and it was amazing. He also tied it upwards into abstract algebra WRT vector spaces. He also taught my abstract algebra where he tied things back into linear algebra. That was an amazing set of classes...

⬐ umanwizard

Matrices are not fundamental or interesting by themselves as just Excel-like grids of numbers. The reason we care about them is because they are a convenient notation for a certain class of functions.

I have to catch a flight so I don't have time to explain this fully, but the key points are:

1/ A "linear function" is a function where each variable in the output is "linear" in all the variables of the input (i.e., a sum of constant multiples of the input variables). e.g. f(x,y) = (x + 3y, y - 2x) is a linear function, but g(x, y) = (x^2, sin(y)) is not.

2/ All linear functions can be represented by a matrix. The `f` I mentioned above corresponds to the matrix:

  [ 1 3
   -2 1 ]

3/ The rules of matrix multiplication are defined so that multiplying by the matrix of a linear function corresponds to applying that function.

For example, again using the definitions above:

  f(7, 8) = (31, -6)

And notice that we get the same thing when we do matrix multiplication:

  [ 1 3   * [ 7      = [ 31
   -2 1]      8 ]        -6 ]

4/ Matrix multiplication also corresponds to function composition. If `f` is as defined above, and `h` is defined by h(x, y) = (-3y, 4x + y), then the matrix for h is

  [ 0 -3
    4  1 ]

and the function `f ο h` you get by applying `h` and then `f` is (you can check this...)

  f ο h(x, y) = (12x, 4x + 7y)

The matrix for this functions happens to be

  [ 12 0
     4 7 ]

But, lo and behold, this matches matrix multiplication:

  [ 1 3    * [ 0 -3    =  [ 12 0
   -2 1 ]      4  1 ]        4 7 ]

4/ Why do we care about linear functions? Well, linear functions are interesting for a lot of reasons, but one in particular is that (differential) calculus is all about approximating arbitrary differentiable functions by linear ones. So you might have some weird function but, if it's differentiable, you know that "locally" it is approximated by some (constant plus a) linear function

I'd highly recommend this set of videos: https://youtu.be/kjBOesZCoqc

⬐ brudgers

Also Gilbert Strang's lectures: https://www.youtube.com/watch?v=ZK3O402wf1c&list=PL49CF3715C...

If you are open to videos, you might be interested in https://www.youtube.com/watch?v=kjBOesZCoqc&index=1&list=PLZ...

Ooooh, these are nice. Here are mine:

Extra History: stories of historical incidents — https://www.youtube.com/watch?v=EbBHk_zLTmY&list=PLhyKYa0YJ_... Real Engineering: mostly materials science — https://www.youtube.com/watch?v=niVguabIhTs&t=33s - Wendover Productions — mostly transportation - https://www.youtube.com/watch?v=NlIdzF1_b5M Tom Scott: a bit of everything — https://www.youtube.com/watch?v=VdmQp9M9jUo - Jay foreman: Urban planning and maps — https://www.youtube.com/watch?v=jjuD288JlCs The Engineer Guy: Manufacturing — https://www.youtube.com/watch?v=xYNX8y6lQMc Practical Engineering: Mostly Civil Engineering — https://www.youtube.com/watch?v=0olpSN6_TCc&list=PLTZM4MrZKf... 3Blue1Brown: Math, visualized to me more intuitive — https://www.youtube.com/watch?v=kjBOesZCoqc

⬐ erikig

Thanks for these but alas - the formatting!

⬐ afarrell

ah drat. I forgot about needing an extra newline. Apologies :/

⬐ jagger27

Extra History and Jay Foreman are new to me. Thank you!

Fror a high-level overview of linear algebra, 3Blue1Brown's youtube series I cannot recommend highly enough.

https://www.youtube.com/watch?v=kjBOesZCoqc&list=PLZHQObOWTQ...

Have you seen the Essence of Linear Algebra video series posted to HN a few days ago? Seeing the geometric transformations animated gives you intuition hard to develop otherwise:

Essence of Linear Algebra (visualized) https://www.youtube.com/watch?v=kjBOesZCoqc&list=PLZHQObOWTQ...

⬐ mindcrime

Yep. Watched the first 3 or 4 of those right after they were posted. Good stuff. I'm not really focusing on Linear Algebra yet, but definitely looking forward to digging into those and the Gilbert Strang ones on LA.

⬐ espeed

The course that follows the MIT calculus course is "Differential Equations" (which is like applied calculus):

MIT Differential Equations: https://www.youtube.com/watch?v=ZvL88xqYSak&list=PLUl4u3cNGP...

Don't overlook mathematical analysis -- real analysis, complex analysis, etc -- that's another big leg of the mathematical stool, with geometrical foundations underpinning it all.

https://en.wikipedia.org/wiki/Mathematical_analysis

https://ocw.mit.edu/courses/mathematics/18-100c-real-analysi...

As you self-study and progress into upper level math, you'll come across abstract and unfamiliar topics you didn't learn about in calculus/algebra -- and sometimes it's hard to pin down what category the topic falls under -- when that happens, the topic will often be related to analysis, group theory, or topology (courses taken by math majors but not as widely known).

See http://nada.kth.se/~axelhu/mapthematics.pdf and http://space.mit.edu/home/tegmark/toe.gif

Crosslinks for all MIT courses: http://crosslinks.mit.edu/topics/?query=subject18.100

See the "Essence of Linear Algebra" (visualized) by the same author -- it should give you more intuition into the nature of the transformations:

Essence of Linear Algebra https://www.youtube.com/watch?v=kjBOesZCoqc&list=PLZHQObOWTQ...

⬐ yamaneko

3Blue1Brown explanation of eigenvectors and eigenvalues is very insightful and intuitive [1]. One of my favorite videos from his channel is "Who cares about topology? (Inscribed rectangle problem)" [2]. They way a Torus and Möbius Strip come up as solution to the problem is so elegant.

[1]: https://www.youtube.com/watch?v=PFDu9oVAE-g&list=PLZHQObOWTQ...

[2]: https://www.youtube.com/watch?v=AmgkSdhK4K8

⬐ mlechha

There's a new topology video out! As cool as the first one!

⬐ espeed

Here is the animation engine used in the videos (written in Python):

Manim: animation engine for explanatory math videos https://github.com/3b1b/manim

⬐ hscells

I always thought he used processing. The fact that he built all the animations with his own library makes his videos way more impressive now.

⬐ adamnemecek

He jokes about it in the series. That he used linear algebra for it too.

⬐ lottin

The introductory video is absolutely right. I studied linear algebra at university but it's been only recently when I decided to re-learn it that I have finally got it, and for that understanding the geometry behind linear algebra is crucial. Now I find myself thinking about problems in terms of matrices and vectors and making all sorts of deductions, even writing mathematical proofs, which I never thought I would.

⬐ throwaway7645

Sounds like you'd enjoy playing around with array programming languages like APL (dyalog, microapl), J, or Q w/ kdb+(kx systems). As one of the oldest paradigms, there are a few open source and proprietary-commercial offerings.

⬐ falloutx

This is probably the best Math Channel on Youtube. I highly recommend watching his Topology videos. Numberphile, Mathloger and Vsauce are other great youtube Channels which I subscribe to.

⬐ DanAndersen

These videos are a treasure and I watch every new video that 3Blue1Brown puts out. They saved me last year when I had a graduate-level numerical linear algebra class and was struggling to grok the true meaning of all this linear algebra stuff (an embarrassing situation for a computer-graphics guy to be in!). Things that had always been "insert formula X to get result Y" started making a lot more sense.

The videos also make me angry because it frustrates me that such explanations were not available to me earlier in my life. What is it about the state of math education that this kind of explanation is not there in every class?

⬐ CamperBob2

What is it about the state of math education that this kind of explanation is not there in every class?

Computational skill is used as a proxy for understanding because educators, just like the rest of us, are lazy-ass human beings. The authors of standardized tests don't care if you know what an eigenvalue is, only that you can calculate one.

Or, put more charitably: teaching math is hard as hell.

Like so many other aspects of our lives, modern math education in the US grew out of a knee-jerk response to a perceived crisis -- the launch of Sputnik, in this case -- that wasn't very well thought out. Schools were required to measure kids' progress in math and science quantitatively, precisely, and repeatably. And just as in other fields, once a measurement becomes a target, it ceases to be a good measurement.

⬐ afarrell

I think the problem is that until recently, the costs of producing and distributing these videos was much higher. With the rise of YouTube, it has become possible for a Salman Khan or John Green to become a celebrity eduvideographer without a lot of capital investment.

One of the flaws of common core is that it seems that the proponents did a poor job of marketing it to the broader adult community. Doing so would have:

1) Given parents the answer to "why is this change happening at all? I learned math just fine as a kid!"

2) Engaged some people in trying to think about the best ways to explain that material and accelerated the formation of a community that gains status with each other by coming up with better and better explanations of the common core curriculum.

⬐ allengeorge

I have to echo what the posters above have already said: I learned linear algebra way back in the day, and it's only now, watching the videos, that I suddenly _got_ matrix multiplication etc. I'm not joking when I say I almost cried with joy. These videos are incredible, and I'm so sad I didn't see them earlier in my life.

⬐ 75dvtwin

Same here, felt like 'crying with joy'. I have been struggling to really understand and internalize eigen vectors for years now (even I used them for some of my lab work). With this visualization, I felt like it had opened another, previously closed, door for me. I would like to donate to this author (and octave's author, on a separate note).

⬐ Dangeranger

3blue1brown's videos are the best I've found for linear algebra and mathematics in general, they are excellent and insightful.

If you value this kind of material please consider supporting via their Patreon page.

https://www.patreon.com/3blue1brown

⬐ afarrell

These explainations are fantastic! Does anyone know of a literature class that examines different technical explainations and analyses why they are successful and where they fail?

⬐ espeed

Bret Victor's essays, demos, and talks focus on this topic:

http://worrydream.com/

⬐ afarrell

So one thing I just noticed: in Video 4 (Matrix Multiplication) when he shifts from just showing geometry to a walkthrough of the numerical operations he begins tracing the paths of i-hat and j-hat. This continues to keep the explanation concrete. In fact, it is almost as if he is a programmer debugging a set of functions and walking the path of a piece of data from through one function call to another.

You can follow this along here: https://www.youtube.com/watch?v=XkY2DOUCWMU&list=PLZHQObOWTQ...

⬐ pzh

I'd also heartily recommend Gilbert Strang's Linear Algebra video lectures (OCW MIT). They seem to have the same goal--to develop a very strong geometric intuition.

⬐ malikNF

Wow thanks for posting this link. I was wondering does anyone know more channels (or any other resource) just like this one, for Statistics and Calculus?

⬐ mindcrime

One of the best channels that I've found for Calculus is:

https://www.youtube.com/channel/UCoHhuummRZaIVX7bD4t2czg

He also has a Statistics series, as well as some pre-calculus / basic algebra stuff.

⬐ nergethic

This is an amazing teacher, great channel for learning calculus: https://www.youtube.com/channel/UCoHhuummRZaIVX7bD4t2czg

⬐ alphajulietmike

Check out Mooculus series on YouTube

⬐ chadcmulligan

These are fun too, not directly calculus but some infinities and series videos https://www.youtube.com/channel/UCOGeU-1Fig3rrDjhm9Zs_wg

⬐ aktiur

Wow, my Saturday afternoon just disappeared.

⬐ sixo

There are great, like everyone 3b1b makes. I'm comfortable with lin alg but I'm skimming them to see what he's chosen to emphasize. I love - for example - that he points out how "span" becomes more interesting in 3d, obv with an example, and the underemphasis on the mechanical operation of matrix multiplication relative to the geometric one.

I do wish the formulas for the dot product and determinant were derived from the geometric explanation, rather than justified with it afterwards. I always appreciated that in classes.

There are some more advanced topics in lin alg that I would have loved to see get the full visual intuitive treatment when I was learning these things.

- SVD, because it's more general and less pathological than eigenvalue decomposition, and often more useful. - A linear transformation as consisting of (I think, it's been a little while) a choice of eigenvectors and eigenvalues, "divided" by the extra degrees of freedom from duplicate eigenvalues. - The "taxonomy" of normal matrices and the polar decomposition (obviously comes after complex matrices)

And there's a nice visualization of the mechanical algorithm of matrix multiplication that looks way more "plausible" than the normal one: draw your two input matrices and your output matrix on grids on 3 sides of a rectangular prism around a corner. Then each value in the output matrix is the dot product of the vectors that intersect at that coordinate, and the whole thing only looks right if all the dimensions match up correctly.

⬐ smnplk

I like how the intro music of each video relaxes me into the subject.

⬐ rnhmjoj

I took a Linear Algebra course last year: the relationship between linear transformations, matrices and basis was carefully explained and also given a clear geometrical interpretation but the determinant was introduced as some magical matrix function with all the property we needed (multilinear, alternating, ...) and the just proceeded to prove its existance and uniqueness. I have never even thought it was related to area before. Also the justification (in chapter 8 part 2) for the formal determinant calculation to obtain the cross product is amazing.

I'm still not sure what the essence of the cross product is: how it is related to divisions algebra (quaternions and octonions) and how bivectors fit in the context of general vector spaces. This was not in the scope of the course however.

⬐ espeed

Other good STEM video channels/series:

Dave Ackley's series "Hyperspace Academy", "Robust First Computing", and "Artificial Life" are well animated: https://www.youtube.com/user/DaveAckley/

Vsause's video on "The Banach–Tarski Paradox": https://www.youtube.com/watch?v=s86-Z-CbaHA (mindblown)

XylyXylyX channel's series on "What is a Tensor?" and "What is a Manifold?": https://www.youtube.com/user/XylyXylyX/playlists

Socratica's series on "Abstract Algebra": https://www.youtube.com/playlist?list=PLi01XoE8jYoi3SgnnGorR...

Mathologer's channel on all-things math: https://www.youtube.com/channel/UC1_uAIS3r8Vu6JjXWvastJg

Ben Garside's series "Vector Spaces": https://www.youtube.com/channel/UCu5cg_Jd9XSJL_CHUskgkGw/pla...

PatrickJMT's channel on calculus, game theory...(too many to list): https://www.youtube.com/user/patrickJMT/playlists

Numenta's (http://numenta.com) series "HTM School" on the Hierarchical temporal memory (https://en.wikipedia.org/wiki/Hierarchical_temporal_memory) model for ANNs: https://www.youtube.com/playlist?list=PL3yXMgtrZmDqhsFQzwUC9...

Dan Shiffman's series "The Nature of Code: Simulating Natural Systems with Processing": https://www.youtube.com/user/shiffman/playlists?shelf_id=6&s...

⬐ majkinetor

Thanks a lot for this nice list.

⬐ aalhour

Thanks a lot for sharing. Have you checked out Socratica's Abstract Algebra series?

YouTube Link: https://www.youtube.com/playlist?list=PLi01XoE8jYoi3SgnnGorR...

⬐ espeed

4th one down :)

⬐ mathgenius

I'm just starting to realize that there are whole other levels of depth of understanding underneath this geometric intuition. So if you manage to grasp what is in these videos, don't stop! It keeps getting deeper and more mysterious, [1][2].

[1] https://en.wikipedia.org/wiki/Rank%E2%80%93nullity_theorem#R...

[2] http://math.ucr.edu/home/baez/week233.html

⬐ nafizh

Wow, thank you so much for posting this link. I was looking for something like this before jumping into theoretical machine learning.

⬐ sndean

It can be pretty hard to sift through, but there's some really good content on YouTube. WelchLabs is another great channel: https://www.youtube.com/user/Taylorns34/videos

Specifically their "Learning to See" series.

⬐ Kenji

Oh wow, I wish I would have watched that 6 years ago. But maybe it only makes sense now because I already learned it all.

⬐ Dowwie

3Blue1Brown makes really great content

⬐ gcoda

I feel like this is changed my life just now. Even functional programming will be more meaningful with this. I want to learn haskell now

⬐ jajool

i wish there were videos about matrix factorization methods.

⬐ elviking

I went to a top school in the US and I got a major in CS without ever taking linear algebra, which in hindsight seems completely crazy. Every major in science or eng. should have this as part of the mandatory curriculum.

⬐ espeed

Hmm...it's been core curriculum in my school's CS department since I was there (almost 20 years ago) -- this is the first time I've seen visualizations like this though.

The next evolution will be to make these type of video lectures/visualizations interactive by implementing the math animation engine in JavaScript/ClojureScript and syncing it with the audio.

⬐ djeunneun

MIND BLOWN!

⬐ melling

Previous discussion: https://news.ycombinator.com/item?id=13051241

Wow, this lecturer is great! I think this is the most intuitive explanation of Kalman filters I've seen yet. I've seen other lecturers try to quickly jump into state space and lose students with big matrices.

I would have paid good money for this if I wasn't already familiar with the material. The clarity is up there with The Essence of Linear Algebra: https://www.youtube.com/watch?v=kjBOesZCoqc

Trading math videos on the Internet--definitely nerds.

check out this playlist[0]. This guy provides intuition behind major LA concepts. Have fun! :) [0] https://www.youtube.com/watch?v=kjBOesZCoqc&list=PLZHQObOWTQ...

It at least cuts down on the amount of time you have to explain the mechanics of it. This is more intuitive to memorize than an algorithm composed of bullet-point instructions. For intuition, I highly recommend https://www.youtube.com/watch?v=kjBOesZCoqc - I think both the intuition and practicing the details should be learned.

The creator of the Triangle of Power (https://www.youtube.com/watch?v=sULa9Lc4pck) and the Essence of Linear Algebra (https://www.youtube.com/watch?v=kjBOesZCoqc). He is now trying to focus full time on online math education.