# Very quick matrix question

1. Apr 3, 2012

### mikedamike

Very quick question.

Im 99% sure that the transpose of a matrix of only diagonal ones is always equal to its original state.

Ie
|1000| |1000| T
|0100| |0100|
|0010| = |0010|
|0001| |0001|

So my question is am i correct ?

2. Apr 3, 2012

### tiny-tim

hi mikedamike!
yes, and it works for any diagonal matrix …

(a)Tii = (a)ii

3. Apr 3, 2012

### HallsofIvy

Staff Emeritus
The definition of "transpose" is that if the elements of A are "$a_{ij}$" then the elements of A^T are $a_{ji}$. So if all non-diagonal elements are 0, we have $a_{ij}= a_{ji}= 0$. And, of course, on the diagonal i= j so we still have $a_{ij}= a_{ji}$.