Show that for any matrix $A_{m \times n}$ , the row rank and column rank are equal
60736
Looking for an intuitive explanation why the row rank is equal to the column rank for a matrix
2109
Max dimension of a subspace of singular $n\times n$ matrices
41436
rank of complex conjugate transpose matrix property proof
48113
Find a basis for the vector space of symmetric matrices with an order of $n \times n$
123151
Find the rank of matrix.
122853
Show that $\operatorname{rank}(A) = \operatorname{rank}(B)$
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.
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 $\det(AA^T)=nk^2.$
17430
If $\operatorname{rank}\left( \begin{bmatrix} A &B \\ C &D \end{bmatrix}\right)=n$ prove that $\det(AD)=\det(BC)$
65395
Prove that if $\operatorname{rank}(T) = \operatorname{rank}(T^2)$ then $R(T) \cap N(T) = \{0\}$
73297
Two idempotent matrices are similar iff they have the same rank
65783
Proving: "The trace of an idempotent matrix equals the rank of the matrix"
121157
Proof verification: column rank = row rank
86940
Proving an inequality in Eigenvalues of a matrix
111031
Matrix rank and linear independence of functions
136329
A matrix is similar to its transpose
31326
Number of $(0,1)$ $m\times n$ matrices with no empty rows or columns