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.

Answer 1

True. Do you need to prove it?

Answer 2

yes

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

I will take a look at the link, thank you