Linear transformations as matrices

Course Q&A Math for Machine Learning Linear Algebra for Machine Learning and Data Sc...
1

In the video Linear transformations as matrices, what it’s trying to tell me in this pic?

image
image964×504 86.7 KB

Are we using any matrix operation here? I don’t get it, what is this operation?
image

2

It is matrix multiply, right? In each case, you are multiplying a 2 x 2 matrix by a 2 x 1 vector to produce the output 2 x 1 vector.

3

Question, how are we getting the incognito matrix?

for example:

1219×599 142 KB

in here the point [0,1] did dot product with [[3,1],[1,2]] = [1,2]
But if [0,1] do dot product with [[0,0],[1,2]] it can also get the same vector[1,2]

4

No it doesn’t. That would give you [0 ,2], right? What is an incognito matrix?

5

like what matrix the vector multiply to to get the vector on the right

image
image830×445 72.5 KB

image
image
why? isn’t (0×0)+(1×1)=0+1=1
and (0×0)+(1×2)=0+2=2?

6

Matrix multiply is not commutative. The operation you show is not what is done on the slide. There they are doing it in the opposite order and that will give you [0, 2] as a column vector. They are solving for M \cdot v which gives the desired output. The order matters.

7

So in what scenario we do v *M? could you give me some example? Or normally the vector linear transformation is always done by M * v

8

This is basically a choice that Prof Luis has made, but that is the way that everyone does it when they are expressing linear transformations as matrix multiplies.