Diagonalization and rank
4952
Let $A$ be a diagonalizable matrix and $\lambda$ be an eigenvalue of A. Prove that rank($\lambda I - A$) = rank(($\lambda I - A)^2$).
5058
Eigenvalues of the rank one matrix $uv^T$
87494
$\operatorname{rank}(T^3) + \operatorname{rank}(T) \geq 2\operatorname{rank}(T^2)$ for finite-dimensional $V$
156877
Rank-one perturbation proof
58476
Why can a matrix whose kth power is I be diagonalized?
33451
Sylvester rank inequality: $\operatorname{rank} A + \operatorname{rank}B \leq \operatorname{rank} AB + n$
59055
Diagonalizable transformation restricted to an invariant subspace is diagonalizable
64517
Prove that row rank of a matrix equals column rank
137890
Diagonalizable Operators and characteristic polynomials
34820
Transpose Operator is diagonalizable?
44383
Finding rank of a matrix depending on parameter a
139087
polar decomposition of a square A when A is not full rank/invertible
115368
Diagonal Subspace of Cartesian Product
65062
Prove $\text{rank}(A) \geq \frac{(\text{tr}(A))^2}{\text{tr}(A^2)}$ when $A$ is Hermitian
10014
Is there a built-in procedure for simultaneous diagonalization of a set of commuting matrices?
30866
Relation between rank and number of distinct eigenvalues of a matrix
119435
Rank of the difference of matrices