This playlist gives a very nice geometric intuition to a lot of the foundational concepts of linear algebra:<p><a href="https://m.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab" rel="nofollow">https://m.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVF...</a>
Really good stuff from what I could tell from a glance at this!
"Linear Algebra Done Right" is a terrific book, though personally I favor Lax's book: "Linear Algebra and its Applications".
I have not studied Terence Tao's notes (which I obtained from AMS's link for "open math notes") <a href="https://www.ams.org/open-math-notes/omn-view-listing?listingId=110650" rel="nofollow">https://www.ams.org/open-math-notes/omn-view-listing?listing...</a>.
Based on what I know of Tao's writing in general, this should be fun.<p>Note that these references have a more "abstract" viewpoint (e.g focusing on "coordinate-free" methods, such as linear operators as opposed to matries as the fundamental object) than that advocated and taught by Strang. I do not know in the end which is better for an absolute beginner.
All I can guarantee is that the abstract viewpoint is definitely needed and far more useful for anyone using math beyond its basics. This includes (but is not limited to) machine learning and optimization.
I gathered the videos into a playlist for better findability: <a href="https://www.youtube.com/playlist?list=PLF9bYy39t4tGBnJ9FjOSFpb6IVchMh5Sv" rel="nofollow">https://www.youtube.com/playlist?list=PLF9bYy39t4tGBnJ9FjOSF...</a>
I like this series by Gilbert Strang:<p><a href="https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/" rel="nofollow">https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra...</a>
I was recently trying to understand wireless channel estimation. So supposedly at the reciever we have to pass the signal through, an inverse channel filter to recover the transmitted signal. A friend of mine asked: what if the channel has no inverse? I had no idea how to respond to this because of my poor intuitive understanding of linear algebra.<p>3blue1brown's video series explained this beautifully as, when the inverse doesn't exist, the transformation packs the input into a lower dimensional space. So in communication terms the transmitted signal is completely lost anyway. So we should look for a better channel to communicate.<p>Now needless to say there is a lot I am probably wrong about, but I'm still very grateful for that excellent video series.
I really think Gilbert Strang's lectures are responsible for creating the impression that linear algebra is hard. I watched that lecture and it was all dry math and very few intuitions.
"Linear algebra done right" is a better book.
Come on we are in 21st century and our intelligence has evolved so that we can understand the 16th century math better :)
If you want a more advanced book I really strongly recommend Matrix Analysis and it's Applications by Carl Meyer. Very clear and concise and the problems are well written. It's my all time favorite math book. But this is really if you want to absorb a lot of more-advanced linear algebra with a lot less fluff and exposition than Strang
Does anyone have a good book for advanced linear algebra? I learned the basics in school - eg. Matrix diagonalization, svd) but I need for ml to really understand things like angle between flats, tensor decomposition, etc
It will be nice if somebody ever does a version of (I) here's the theory behind a linear algebra equation, and then, (ii) here's a real world application.