Proving Symmetry of A + A(Transpose) for Any Square Matrix A

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SUMMARY

The discussion focuses on proving that the expression A + AT is symmetric for any square matrix A. A symmetric matrix is defined as one where A = AT. The participants clarify that the proof does not assume A is symmetric initially and emphasize the importance of correctly defining symmetric matrices. The conclusion is that A + AT is indeed symmetric, as it satisfies the condition of symmetry by construction.

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Homework Statement


Show that A + A(transpose) is symmetric for any square matrix A.

Homework Equations


A symmetric matrice is equal to A=A(transpose)


The Attempt at a Solution



I said A + A(transpose)
= A(transpose) + A(transpose)
= (A + A) (transpose)
= A + A

I don't know what else to do
 
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It looks like you're assuming that A is symmetric right at the start, which isn't information that you're given.

Start with the definitions of AT and symmetric matrix.

The definition you show for a symmetric matrix isn't right - I think you want this:
A symmetric matrix A is such that A = AT. (A matrix can't be "equal" to an equation.)
 

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