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Very quick matrix question

by mikedamike
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mikedamike
#1
Apr3-12, 03:51 AM
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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tiny-tim
#2
Apr3-12, 05:24 AM
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P: 26,157
hi mikedamike!
Quote Quote by mikedamike View Post
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
HallsofIvy
#3
Apr3-12, 08:04 AM
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PF Gold
P: 39,348
The definition of "transpose" is that if the elements of A are "[itex]a_{ij}[/itex]" then the elements of A^T are [itex]a_{ji}[/itex]. So if all non-diagonal elements are 0, we have [itex]a_{ij}= a_{ji}= 0[/itex]. And, of course, on the diagonal i= j so we still have [itex]a_{ij}= a_{ji}[/itex].


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