Rank of a matrix $A$ such that $A + A^T = 0$
94639
Proof that the rank of a skew-symmetric matrix is at least $2$
55377
Non-zero eigenvalues of $AA^T$ and $A^TA$
87494
$\operatorname{rank}(T^3) + \operatorname{rank}(T) \geq 2\operatorname{rank}(T^2)$ for finite-dimensional $V$
130799
Matrix of rank 1; show that $A^2=cA$ for some scalar $c$.
6905
Rank of product of a matrix and its transpose
27821
A problem on rank of $A$ and $\operatorname{adj}(A)$
29788
Eigenvalues of a matrix whose square equals its transpose
98273
minimal polynomial of powers of a matrix
51800
We have matrix $A\in M_{n-1\times n}(\mathbb Z)$ so that the sum of entries in each row is zero. Prove that $\det(AA^T)=nk^2.$
129564
Show that $A$ is an invertible matrix if $\left(A+I\right)^3=0$ and find $A^{-1}$
18282
Finding the minimal polynomial, the eigenvalues, and the characteristic polynomial of $T(A)=A+A^t$
46128
Representation of Matrix with Rank 1
131611
$A^TA$ is always a symmetric matrix?
140252
Matrices - Conditions for $AB+BA=0$
65395
Prove that if $\operatorname{rank}(T) = \operatorname{rank}(T^2)$ then $R(T) \cap N(T) = \{0\}$
7205
Find the determinant of $A + I$, where $A$ is a real matrix such that $AA^{\top}=I$ and $\det A<0$.
65628
what happens to rank of matrices when singular matrix multiply by non-singular matrix??