
#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

Sci Advisor
HW Helper
Thanks
P: 26,167

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



#3
Apr312, 08:04 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,904

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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