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 **R**^{n}(lefthand side) to **R**^{m}(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(A ^{T})** and the blue is the null space of A transposed –

**N(A**. The drawing denotes that the null space is perpendicular to the row space, and also the solution of

^{T})**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(A**, and n = dim

^{T})**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.)

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