suppose $tr(A^k) = tr(B^k)$ for all $k$=$1,2,....$. why $A$ and $B$ are same characteristic polynomial? .
71040
If $ \operatorname{Tr}(M^k) = \operatorname{Tr}(N^k)\;\forall 1\leq k \leq n$, then how do we show the $M$ and $N$ have the same eigenvalues?
106493
Coefficients of characteristic polynomial of a matrix
116389
If $\exp(t(A + B)) = \exp(tA) \exp(tB)$ for all $t \geq 0$ then $A,B$ commute
41514
Let $trcA=0$.why $A=M+N$ where $M$ and $N$ are nilpotent matrices?
83475
Prove Or Disprove: tr(AB)=tr(A)*tr(B)
143608
Show the Trace$(B)^{2} \leq$ nTrace$(B^{T}B)$
77667
A and B is similar ⇒ $A^T$ is similar to $B^T$.
157087
Can anyone explain why $a^{b^c} = a^{(b^c)} \neq (a^b)^c = a^{(bc)}$
145507
Is $K[a,b]=K(a,b)$ for algebraic $a, b$?
76694
Proving that $UT=TU$ iff $U=g(T)$ for some polynomial $g$
48906
Prove that T is diagonalizable if and only if the minimal polynomial of T has no repeated roots.
56817
How do you get \mathbb{1} to work (characteristic function of a set)?
126064
What are examples of two non-similar invertible matrices with same minimal and characteristic polynomial and same dimension of each eigenspace?
94383
Prove that $A^TD-C^TB=I$
139685
If $A^2$ and $B^2$ are similar matrices, do $A$ and $B$ have to be similar?
153480
Roots of a characteristic equation. Can Mathematica solve it?
101861
How do you prove that $tr(B^{T} A )$ is a inner product?