Question

Find the matrix that transforms the standerd basis of c3 to the vector

Answer 1

I know that in order to find transformation matrix with respect to a basis, I need to apply the transformation to said basis and the result is the column of the transformation matrix.

But what happens when the linear transformation is applied to matrices and not vectors? then the map is also a matrix. How am i suppose to write the matrix as a column?

more specifically, I need to find the transformation matrix of T(( a b c d ))=( 2ia b+ci c+bi 2id )

T:M2(C)−>M2(C).

so with respect to standard basis:

T(( 1 0 0 0 ))=( 2i 0 0 0 ) what does this mean? Is the first column of the transformation matrix ( 2i 0 0 0 )? That makes no sense.