I am a lifetime math fan, and I found a wonderful education video for Linear Algebra.
One day, I was looking around several math lectures in the internet, and I incidentally encountered this Prof. Gilbert Strang’s lecture. I was so drawn in to the course as well as the way he talks, that I watched the whole course for the next three months and finished it! And also bought his well-known book and started reading it including all the well-designed problems in it. – “Introduction to Linear Algebra, Fifth Edition (Gilbert Strang) “
I love his books and chalk talks because he uses a lot of actual numbers(1, 2, 3, not x, y) and examples(statistics and physics applications) first to lead us naturally to crystalize them into theorems. I was impressed by the power of hand calculation and concrete examples. My Linear Algebra teacher 30 years ago used symbols and chains of remmas, proofs and theorems, and I never got this feeling of “understanding” at the time. I got so into the books, the videos and the great teacher Gilbert Strang!
The other day, I wrote an email to him just to say I was a big fan of him, then he replied to me the next day. And moreover, for my birthday he sent me a hand-written letter with his recent updates on his new book! (I knew later it was a surprise that, Satomi, a friend of mine, secretly planned and asked him to, wow!)
So, in order to show our deep appreciation to him, we made T-shirts! The drawing on the T-shirt is the transformation A, and the solution x of Ax = b and the four subspaces(explained in the footnote) with his likeness hand-drawn by Satomi, .
I’m sending some of the T-shirts to him, soon. Thank you, Prof. Strang!
I’m a software developer and just remembered I implemented a software library called, vecmath, which supports 3D graphics a while ago, where I coded LU and SVD… I was meant to meet him!
(footnote: the Four Subspaces)
I try to explain a bit about the math here … Think about a linear equations Ax = b where A maps Rn(lefthand side) to Rm(righthand side). The yellow area in the right is the column space(image) of the transformation A – C(A), the green in the left is the null space(kernel) – N(A) which is mapped to 0(solutions of Ax = 0). The red area is the row space – C(AT) and the blue is the null space of A transposed – N(AT). The drawing denotes that the null space is perpendicular to the row space, and also the solution of Ax = b is the addition of a particular solution in the row space and any linear combinations of vectors from null space. And most importantly, rank of A equals the dimension of C(A) and also C(AT), and n = dim C(A) + dim N(A). His fans will surely understand! See Fundamental theorem of Linear Algebra.
(afternote: I drew a Matrix World picture with Professor Gilbert Strang and also Graphic note.)