# Verify that any square matrix is a linear operator when considered as a linear map.

1. Oct 9, 2011

### jinksys

1. The problem statement, all variables and given/known data

Verify that any square matrix is a linear operator when considered as a linear transformation.

2. Relevant equations

3. The attempt at a solution

If a square matrix A$\in$ℂ$^{n,n}$ is a linear operator on the vector space C$^{n}$, where n ≥ 1, then the square matrix A is of the correct dimension to be a linear transform from C->C.

2. Oct 9, 2011

### HallsofIvy

Staff Emeritus
Re: Verify that any square matrix is a linear operator when considered as a linear ma

Except for the rather trivial statement about dimension, I see no attempt at this problem- the question is to show that it is linear.

3. Oct 9, 2011

### jinksys

Re: Verify that any square matrix is a linear operator when considered as a linear ma

Could I get a push in the right direction?

4. Oct 9, 2011

### Deveno

Re: Verify that any square matrix is a linear operator when considered as a linear ma

show it preserves sums and scalar multiples....