Proving that an $m \times n$ matrix has rank 1
34043
A rank-one matrix is the product of two vectors
31116
Matrix given by $a_{ij} = 1/(i+j)$ is non-singular.
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 $\det(AA^T)=nk^2.$
2109
Max dimension of a subspace of singular $n\times n$ matrices
122305
Proof of matrix norm property: submultiplicativity
4952
Let $A$ be a diagonalizable matrix and $\lambda$ be an eigenvalue of A. Prove that rank($\lambda I - A$) = rank(($\lambda I - A)^2$).
127591
How to prove that the collection of rank-k matrices forms a closed subset of the space of matrices?
108012
A matrix $M$ that commutes with any matrix is of the form $M=\alpha I$
82295
Showing that the minimal polynomial of an $n \times n$ matrix has degree at most $n$ without using the Cayley-Hamilton Theorem
15202
the root of $N$th transpose matrix
147797
If $A$ is an invertible matrix, then the column span of $A$ equals $F^{n\times1}$
39746
How to prove that given set is a connected subset of the space of matrices?
41436
rank of complex conjugate transpose matrix property proof
48839
Show that the order of $a\times b$ is equal to $nm$ if gcd(n,m)=1
55820
If $A$ is an $n \times n$ matrix and $ A^2 = 0$, then $\text{rank}(A)\le n/2$.
27474
A square matrix $n \times n$ is an invertible matrix iff the rank of the matrix is $n$.
4509
Proof that an involutory matrix has eigenvalues 1,-1