Show that $r$ is the rank of the $n$x$n$ matrix $A\iff A$ has a nonsingular $r$x$r$ submatrix
48660
Proof that determinant rank equals row/column rank
28460
Show matrix is nilpotent
122853
Show that $\operatorname{rank}(A) = \operatorname{rank}(B)$
67058
Prove that $\text{rank}(X^TX)=\text{rank}(X)$
65628
what happens to rank of matrices when singular matrix multiply by non-singular matrix??
33451
Sylvester rank inequality: $\operatorname{rank} A + \operatorname{rank}B \leq \operatorname{rank} AB + n$
127127
Prove condition number of a invertible matrix is atleast one
11895
If $AB=0$ prove that $\mathrm{rank}(A)+\mathrm{rank}(B)\leq n$
43000
Show $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A+B)$
135171
Under what conditions is the difference between a rank $1$, postive semidefinite matrix and a hermitian matrix positive semidefinite?
156877
Rank-one perturbation proof
18297
Suppose that each of the row sums of an $n\times n$ matrix $A$ is equal to zero. Show that $A$ must be singular.
86940
Proving an inequality in Eigenvalues of a matrix
34536
Columns of matrix $A_{m \times n}$ span $\mathbb{R}^{m}$
57543
Show that a matrix is nilpotent.
74611
$\operatorname{Adj} (\mathbf I_n x-\mathbf A)$ when $\operatorname{rank}(\mathbf A)\le n-2$
65395
Prove that if $\operatorname{rank}(T) = \operatorname{rank}(T^2)$ then $R(T) \cap N(T) = \{0\}$