Prove $XX^T$ and $X^T X$ have same eigenvalues with same multiplicity
31606
Do matrices $ AB $ and $ BA $ have the same minimal and characteristic polynomials?
105910
How to prove that $[G:xHx^{-1}] = [G:H]$ given $H \le G$?
52528
Showing that minimal polynomial has the same irreducible factors as characteristic polynomial
36613
Prove that simultaneously diagonalizable matrices commute
103087
What is the duality relationship between eigensystems of X X' vs X' X?
29788
Eigenvalues of a matrix whose square equals its transpose
7457
Prove that $J^+AJ$ has positive eigenvalues
49438
Prove that $X^\ast$ separable implies $X$ separable
40805
Solve $u_t=u_{xx}+u_x$
12104
How to prove this result involving the quotient maps and connectedness?
30665
Elegant proofs that similar matrices have the same characteristic polynomial?
95717
Same eigenvalues, but not similar
61538
Given a square matrix $A$, both $AA^T$ and $A^TA$ are symmetric
99585
Do the non-zero eigenvalues of AB and BA have the same algebraic multiplicity (for AB and BA not square)?
14161
Proof of when is $A=X^TX$ invertible?
104424
If each eigenvalueof $A$ is either $+1$ or $-1$ $ \Rightarrow$ $A$ is similar to ${A^{ - 1}}$
120933
A is similar to $A^k$, then each eigenvalue of $A$ is a root of unity