How can I obtain the generic matrix T such that hat(X)=TX with: hat(X)=[[a,0],[c,0],[0,b],[0,d]] and X=[[a,c],[b,d]]

kadirsmr9d 2022-09-14 Answered
How can I obtain the generic matrix T such that X ^ = T X with:
X ^ = [ a 0 0 b c 0 0 d ]
and
X = [ a b c d ]
I did several try without obtaining the result I needed.
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Answers (2)

Illuddybopylu
Answered 2022-09-15 Author has 17 answers
Is X is invertible? Then just multilpy X 1 at right of both side of equation.Then T will be X ^ X 1

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Staffangz
Answered 2022-09-16 Author has 1 answers
There is no such T that's independent of the entries of X.If there were such T, then consider the effect of swapping the columns of X,
X = [ b a d c ] = X [ 0 1 1 0 ]
On one hand, T was assumed to be generic and would transform X′ to the same format:
T X = [ b 0 0 a d 0 0 c ]
On the other hand, TX′ should be like TX but with swapped columns:
T X = T X [ 0 1 1 0 ] = [ a 0 0 b c 0 0 d ] [ 0 1 1 0 ] = [ 0 a b 0 0 c d 0 ]
And note how the zero entries are at different positions.

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