# Homework Help: Is this a diagonal matrix

1. Dec 26, 2003

### denian

diagonal matrix is a matrix with each element is0 excep for elements on the major diagonal.

so, does it mean that

( 2 0 0
0 0 0
0 0 3 )

is not a diagonal matrix??

2. Dec 26, 2003

### Hurkyl

Staff Emeritus
A (square) matrix is diagonal iff the nondiagonal entries are zero.

The diagonal entries are permitted to be zero as well, so this matrix is diagonal, with diagonal entires 2, 0, and 3:

$$\left( \begin{array}{ccc} 2&0&0 \\ 0&0&0 \\ 0&0&3 \end{array} \right)$$

(Yes, I am using this post as an excuse to get more practice writing in LaTeX. )

3. Dec 26, 2003

### HallsofIvy

To extend Hurkyl's answer, the conditional in the Hurkyl's definition is:
" the nondiagonal entries are zero". That says nothing about numbers on the diagonal which may be zero or non-zero,