Proof: rank(A) ≤ k if A is the sum of k matrices of rank 1
59396
Show that the rank of $A+B$ is no more than the sum of the ranks of $A$ and $B$
128990
Prove that, at least one of the matrices $A+B$ and $A-B$ has to be singular
86940
Proving an inequality in Eigenvalues of a matrix
156877
Rank-one perturbation proof
27821
A problem on rank of $A$ and $\operatorname{adj}(A)$
27248
If $A$ is an $m \times n$ matrix, prove that $Ax=0$ has infinite solutions $\iff$ $\text{rank}(A)<n$
135171
Under what conditions is the difference between a rank $1$, postive semidefinite matrix and a hermitian matrix positive semidefinite?
122305
Proof of matrix norm property: submultiplicativity
46128
Representation of Matrix with Rank 1
27474
A square matrix $n \times n$ is an invertible matrix iff the rank of the matrix is $n$.
44383
Finding rank of a matrix depending on parameter a
35897
Proof of: $AB=0 \Rightarrow Rank(A)+Rank(B) \leq n$
64517
Prove that row rank of a matrix equals column rank
136737
Proof by Induction for inequality, $\sum_{k=1}^nk^{-2}\lt2-(1/n)$
114575
If $\sum_{i=1}^k \dim F_i > n(k-1)$ then $\cap_{i=1}^k F_i \neq \{0\}$
130498
Linear algebra proof regarding matrices
55820
If $A$ is an $n \times n$ matrix and $ A^2 = 0$, then $\text{rank}(A)\le n/2$.