Question #1860

Prove that tr(A.A[sup]T[/sup])=tr(A[sup]T[/sup].A) for every matrix A.

Expert's answer

Aij = A^{T}ji

tr(A.A^{T}) =∑ ∑A_{ij }A_{ij} = ∑ A_{ij}^{2}

tr(A^{T}.A) =∑ ∑A_{ji }Aji = ∑ ∑A_{ij }Aij = ∑ A_{ij}^{2}

tr(A.A

tr(A

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