Very quick matrix question

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.

tiny-tim

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

Code:

              |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)^T_ii = (a)_ii

HallsofIvy

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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mikedamike	Very quick matrix question Tweet 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.

HallsofIvy Recognitions: Gold Member Science Advisor Staff Emeritus	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].