Can a matrix with all zero diagonal entries be diagonalized?

[pizzamakeren]

Homework Statement

A simple question about the topic diagonal matrix and diagonalization.

Relevant Equations

No equations

A quick and simple question. I just realized that this has been posted in the wrong section, but ill give it a try anyway. Does anyone know if it's possible to diagonalize a hollow matrix? What i mean by a hollow matrix is a matrix with only zero entries along the diagonal.

 

[kuruman]

Why not? Try diagonalizing$$\begin{pmatrix}
0 & 1 \\
1 & 0
\end{pmatrix}$$and see what you get.

 

[Orodruin]

Sometimes. It depends on the matrix.
\begin{pmatrix}
0 & 0 \\ 0 & 0
\end{pmatrix}
is obviously diagonalizable.