A proof for a theorem related to rank and matrix product.
10483
Prove Sylvester rank inequality: $\text{rank}(AB)\ge\text{rank}(A)+\text{rank}(B)-n$
27821
A problem on rank of $A$ and $\operatorname{adj}(A)$
75211
Theorem about positive matrices
72551
Proof that $\rho = \pm1$ implies linear combination
15452
Proving determinant product rule combinatorially
38945
On the proof that the product of diagonal matrices is a diagonal matrix?
4952
Let $A$ be a diagonalizable matrix and $\lambda$ be an eigenvalue of A. Prove that rank($\lambda I - A$) = rank(($\lambda I - A)^2$).
6905
Rank of product of a matrix and its transpose
121157
Proof verification: column rank = row rank
120065
Niven’s theorem proof.
146847
Given a square matrix A of order n, prove $\operatorname{rank}(A^n) = \operatorname{rank}(A^{n+1})$
35897
Proof of: $AB=0 \Rightarrow Rank(A)+Rank(B) \leq n$
45585
Proof of Steinitz Theorem
75117
$\mathrm{rank}(AB-BA)=1$ implies $A$ and $B$ are simultaneously triangularisable
141015
Proof of orthogonal matrix
146984
Prove: Full Rank and a solution os linear system
65062
Prove $\text{rank}(A) \geq \frac{(\text{tr}(A))^2}{\text{tr}(A^2)}$ when $A$ is Hermitian