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

Question

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

zzr0ck3r · Answer

True. Do you need to prove it?

chrisplusian · Answer

yes

chrisplusian · Answer

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

zzr0ck3r · Answer

https://in.answers.yahoo.com/question/index?qid=20100824085905AAThbDi

chrisplusian · Answer

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

chrisplusian · Answer

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

chrisplusian · Answer

I will take a look at the link, thank you