/sci/ - Science & Math » Thread #11464212

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Can you multiply a Matrix (A) by a Matrix (B) to get the transposed of A?

Anonymous Thu 12 Mar 22:40:23 2020 No.11464212 View Reply Original Report

Quoted By: >>11464226 >>11464237 >>11464282

If so what would be the properties of the Matrix A and B?

Anonymous

Anonymous Thu 12 Mar 2020 22:41:05 No.11464213 Report

Quoted By:

I know this seems like a homework question but I genuinely want to know

Anonymous

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Anonymous Thu 12 Mar 2020 22:46:15 No.11464226 Report

Quoted By:

>>11464212
$AB=A^T$
$B = A^{-1} A^T$
Ask this stuff in sqt, for Christ's sake.

Anonymous

Anonymous Thu 12 Mar 2020 22:46:37 No.11464230 Report

Quoted By: >>11464277

If there were such a T, we would have $T = T X I = I^T = I$ , where $I$ is the identity.
But that would mean that $A = I X A = T X A = A^T$ for all matrices A i.e all matrices are their tranpose.

So no, you can't.

Anonymous

Anonymous Thu 12 Mar 2020 22:50:30 No.11464237 Report

Quoted By:

>>11464212

Linear algebra proofs like this are really easy if you just write down the question in terms of matrix multiplication and use the properties given by your textbook, idk why you'd make a thread.

Anonymous

Anonymous Thu 12 Mar 2020 23:10:57 No.11464277 Report

Quoted By:

>>11464230
He didn't require the B to be the same for all matrices

Anonymous

Anonymous Thu 12 Mar 2020 23:12:50 No.11464282 Report

Quoted By:

>>11464212
is transpose a linear operation?
does it satisfy T(aA + bB) = aT(A) + bT(B)?
if so, then since matricies are finite dimensional vector spaces, then yes, you can construct a matrix to do that.

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