query: Do $\sqrt{A}BA^*B\sqrt{A}$ and $ABA^*B$ have the same eigenvalues?
positive_passages.docid: 31606
positive_passages.text: Do matrices $ AB $ and $ BA $ have the same minimal and characteristic polynomials?
negative_passages.docid: 98855
negative_passages.text: Prove $aba^{-1}b^{-1}\in{N}$ for all $a,b$
negative_passages.docid: 154666
negative_passages.text: similar matrices have same eigenvalue... stuck
negative_passages.docid: 34973
negative_passages.text: Is it true that the order of $ab$ is always equal to the order of $ba$?
negative_passages.docid: 59402
negative_passages.text: Comparing Eigenvalues of Positive Semidefinite Matrices
negative_passages.docid: 158724
negative_passages.text: Show that $B$ is diagonalizable if If $AB=BA$ and $A$ has distinct real eigenvalues
negative_passages.docid: 17032
negative_passages.text: If $ab=ba$, Prove $a^2$ commutes with $b^2$
negative_passages.docid: 136448
negative_passages.text: $ABAB=0_{n\times n}$, then must $BABA$ be $0_{n\times n}$?
negative_passages.docid: 111366
negative_passages.text: Does there exist a symmetric matrix $A$ such that $2^{\sqrt{n}}\le |\operatorname{Tr}(A^n)|\le2020 \ \cdot 2^{\sqrt{n}}$ for all $n$
negative_passages.docid: 92744
negative_passages.text: These two operators commute...but their eigenvectors aren't all the same. Why?
negative_passages.docid: 66709
negative_passages.text: Are the matrix products $AB$ and $BA$ similar?
negative_passages.docid: 72092
negative_passages.text: If $A^2 = I$, $B^2=I$ and $(AB)^2=I$, then $AB = BA$
negative_passages.docid: 54099
negative_passages.text: What are the eigenvalues of $\operatorname{ad}x$?
negative_passages.docid: 127799
negative_passages.text: Eigenvalues of symmetric matrices are real without (!) complex numbers
negative_passages.docid: 8920
negative_passages.text: There exists $C\neq0$ with $CA=BC$ iff $A$ and $B$ have a common eigenvalue
negative_passages.docid: 95717
negative_passages.text: Same eigenvalues, but not similar
negative_passages.docid: 129977
negative_passages.text: Prove that $\lambda_1^2$, $\lambda_1\lambda_2$ and $\lambda_2^2$ are eigenvalues of matrix $A$