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Very quick matrix questionby mikedamike
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#1
Apr312, 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. 


#2
Apr312, 05:24 AM

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P: 26,157

hi mikedamike!
(a)^{T}_{ii} = (a)_{ii} 


#3
Apr312, 08:04 AM

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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 nondiagonal 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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