- #1

patric44

- 272

- 37

- TL;DR Summary
- does the matrix of the linear transformation should have the same dimension of the vector space?

hi guys

I was trying to find the matrix of the following linear transformation with respect to the standard basis, which is defined as

##\phi\;M_{2}(R) \;to\;M_{2}(R)\;; \phi(A)=\mu_{2*2}*A_{2*2}## ,

where ##\mu = (1 -1;-2 2)##

and i found the matrix that corresponds to this linear transformation this 4*4 matrix , given by

$$\phi =(1\;0\;-2\;0;0\;1\;0-2;-1\;0\;2\;0;0 -1\;0\;2) $$

is there is some wrong here or the matrix should be 4*4

I was trying to find the matrix of the following linear transformation with respect to the standard basis, which is defined as

##\phi\;M_{2}(R) \;to\;M_{2}(R)\;; \phi(A)=\mu_{2*2}*A_{2*2}## ,

where ##\mu = (1 -1;-2 2)##

and i found the matrix that corresponds to this linear transformation this 4*4 matrix , given by

$$\phi =(1\;0\;-2\;0;0\;1\;0-2;-1\;0\;2\;0;0 -1\;0\;2) $$

is there is some wrong here or the matrix should be 4*4