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)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F78ec8164-41c7-43f1-86ef-2d717029e4a1%2F15d683ea-ed64-413c-9b00-c074234305bf%2F78vkbyk_processed.jpeg&w=3840&q=75)
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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