The trace of a nxn matrix A is defined as the sum of its diagonal entries:...

 

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The trace of a nxn matrix A is defined as the sum of its diagonal entries: 71 trA = Σ aii. i=l Let A, B be nxn matrices. Prove the following: (a) trA = tr(AT). (b) tr(A + B) = trA + trB. (c) tr(AB) = tr(ΒΑ) [Hint: use the fact that you can "swap" the indices of summation as follows ΣΣ CM = -ΣΣ Cit i=1 k=1 k=1#=1 The trace of a nxn matrix A is defined as the sum of its diagonal entries: 71 trA = Σ aii. i=l Let A, B be nxn matrices. Prove the following: (a) trA = tr(AT). (b) tr(A + B) = trA + trB. (c) tr(AB) = tr(ΒΑ) [Hint: use the fact that you can "swap" the indices of summation as follows ΣΣ CM = -ΣΣ Cit i=1 k=1 k=1#=1

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4 matrix A is define as its digonal entries n face A Ait Trace of ... View the full answer