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Prove: if A and B are nxn matrices, then

tr(A+B)= tr(A)+tr(B)

Jul 24th, 2015

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Tr(A+B) = SUM( [A+B]i,i ) 


= SUM( [A] i,i + [B]i,i ) 


= SUM( [A]i,i ) + SUM( [B]i,i )      (commutative property)


= tr(A) + tr(B).

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Jul 24th, 2015

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