Question

Linear algebra,

can you please tell me whats a symmetric and skew symmetric matrix ?

Thanks a lot

Answer 1

1/symmetric matrix is a matrix satisfies A = \(A^T\) for example : \(A = \left[\begin{matrix}1&2\\2&1\end{matrix}\right]=A^T=\left[\begin{matrix}1&2\\2&1\end{matrix}\right]\)
2/skew symmetric is a matrix satisfies -A= \(A^T\). A skew symmetric always has 0 on its main diagonal .
\(A = \left[\begin{matrix}0&1\\-1&0\end{matrix}\right]\)\(\rightarrow -A = \left[\begin{matrix}0&-1\\1&0\end{matrix}\right]\)
\(A^T=\left[\begin{matrix}0&1\\-1&0\end{matrix}\right]\)
you can see -A = \(A^T\)
They are different, right?

Answer 2

I see, thanks !