Trace of a Matrix Using the following definition, prove the properties of the trace in Problems 1-3.

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Trace of a Matrix Using the following definition, prove the properties of the trace in Problems 1-3.
The trace of an n x n matrix A = [aij], denoted Tr A, is the sum of the diagonal elements:

1. Tr(A+B) = TrA + TrB
2. Tr(cA) = cTrA
3. Tr (AT) =Tr A?

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Differential Equations and Linear Algebra

ISBN: 978-0131860612

2nd edition

Authors: Jerry Farlow, James E. Hall, Jean Marie McDill, Beverly H. West

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Question Posted: May 26, 2016 05:58 AM

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Trace of a Matrix Using the following definition, prove the properties of the trace in Problems 1-3.

Question:

α Σ = aji + a22 + akk. + ann = k=1

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Trace of a Matrix 1 TrA B TrA TrB TrA B a 11 b 11 a n...View the full answer

Differential Equations and Linear Algebra

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