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Using index notation, show that the trace is cyclic, i.e. that for any number m of N × N matrices M(1), M(2),..., M(m), the following holds true: Tr ( M (1) M (²) ... M(m)) = Tr (M(m) M(¹) M (²) ... M(m−1)) (1)

Using index notation, show that the trace is cyclic, i.e. that for any number m of N × N matrices M(1), M(2),..., M(m), the following holds true: Tr ( M (1) M (²) ... M(m)) = Tr (M(m) M(¹) M (²) ... M(m−1)) (1)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 52E
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Using index notation, show that the trace is cyclic, i.e. that for any number m of N × N matrices M(1), M(2),..., M(m), the following holds true: Tr ( M (1) M (²) ... M(m)) = Tr (M(m) M(¹) M (²) ... M(m−1)) (1)
Transcribed Image Text:Using index notation, show that the trace is cyclic, i.e. that for any number m of N × N matrices M(1), M(2),..., M(m), the following holds true: Tr ( M (1) M (²) ... M(m)) = Tr (M(m) M(¹) M (²) ... M(m−1)) (1)
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