is this a diagonal matrix

[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??

[Hurkyl]

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. [:)])

[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,

Your statement:
"each element is 0 except for elements on the major diagonal."
is a slightly ambiguous way of saying the same thing.

The ambiguity could be removed by saying:
"each element is 0 except possibly for elements on the major diagonal."

[denian]

all righttt.. thank you.