# Very quick matrix question

by mikedamike
Tags: matrix
 P: 28 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 ? Thanks in advance.
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P: 26,148
hi mikedamike!
 Quote by 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 ? Thanks in advance.
yes, and it works for any diagonal matrix …
(a)Tii = (a)ii
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,549 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 $a_{ij}= a_{ji}$.

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