Question

Whats the difference between the kernel(T) of a transformation T and a of a matrix transformation T_A?

Answer 1

I know that the kernel of transformation T_A is also the nullspace but then what is the kernel of a transformation T?

Answer 2

A matrix is a linear transformation, but written with respect to a basis for the source space and a basis for the target space.

The kernel of the transformation is the same as the kernel of the matrix. However, for the matrix the vectors in both spaces are written as coordinate vectors where each component represents a coefficient in a linear combination of basis vectors.

Answer 3

Why does my text book say like the kernel of T is a subspace of R^n

Answer 4

for a linear transformation?

Answer 5

and then sometimes it says it's the nullspace

Answer 6

Kernel is just another name for nullspace.

Answer 7

for both matrix transformation and transformation T? Do I need to show it's closed under addition and multiplication each time?

Answer 8

What do you mean?

Answer 9

Okay nvm I think I get it you're saying that the kernel is the nullspace, so if it ask to find kernel just find the nullspace?

Answer 10

If you are referring to the linearity of a transformation
T(au + v) = aT(u) + T(v)

You only need to prove this if you are asked to.

Answer 11

But for like this question The orthogonal projection T on the xy space

Answer 12

I'm not given any value sbut how would I still find the kernel

Answer 13

Once you setup the transformation matrix the kernel is all \(x\) such that \(Ax = 0\)