## chrisplusian one year ago If "A" is an nxn matrix show that "A" can be written as the sum of a symmetric matrix and a skew symmetric matrix.

1. zzr0ck3r

True. Do you need to prove it?

2. chrisplusian

yes

3. chrisplusian

I have a definition in my textbook, and it goes like this.....

4. zzr0ck3r
5. chrisplusian

$A = V+S, where V= \frac{ 1 }{ 2 }(A + A^T), and S = \frac{ 1 }{ 2 }(A - A^T)$

6. chrisplusian

I know I can use this but I am wondering if there is another way generically that I can show this is true. I am not supposed to use actual numbers in any proofs, so I can't just do these operations to a matrix and show it works out

7. chrisplusian

I will take a look at the link, thank you