Let $A\in M_n(\mathbb{Q})$ with $A^k=I_n$. If $j$ is a positive integer with $\gcd(j,k)=1$, show that $ \operatorname{tr}(A)= \operatorname{tr}(A^j)$.

score 234 · Answer 9 · 2026-03-26 17:56:31

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score 746 · Answer 10 · 2019-01-16 03:12:10

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score 569 · Answer 11 · 2019-01-16 03:29:04

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score 809 · Answer 13 · 2019-01-19 01:53:12

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Show that the $\text{Tr}(A)^2 = \text{Tr}(A^2)+\text{Sum of Eigenvalues} $

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score 242 · Answer 14 · 2019-01-20 19:09:44

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How to choose $B$ to have $ \operatorname{trace}(H) \ge \operatorname{trace}(B^{\top}HB)$?

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score 1.9k · Answer 15 · 2019-01-21 08:52:04

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$ \langle A, B\rangle := \operatorname{Tr}(AB^{∗}) $ Inner Product in $\mathbb{C} $?

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