rank of $A = (a_{ij}) \in \mathbb{R}^{n \times n}$ where $a_{ij} := i +j \quad \forall 1 \leq i, j \leq n$.
45532
Let $A$ be a $n\times n$ matrix with entries $a_{ij}=i+j $ . Calculate rank of $A$
87494
$\operatorname{rank}(T^3) + \operatorname{rank}(T) \geq 2\operatorname{rank}(T^2)$ for finite-dimensional $V$
27248
If $A$ is an $m \times n$ matrix, prove that $Ax=0$ has infinite solutions $\iff$ $\text{rank}(A)<n$
123151
Find the rank of matrix.
2798
A and B are nxn matrices, $A =B^TB$. Prove that if rank(B)=n, A is pos def, and if rank(B)<b, A is pos semi-def.
118283
Show that if $A^{n}=I$ then $A$ is diagonalizable.
121157
Proof verification: column rank = row rank
65783
Proving: "The trace of an idempotent matrix equals the rank of the matrix"
74611
$\operatorname{Adj} (\mathbf I_n x-\mathbf A)$ when $\operatorname{rank}(\mathbf A)\le n-2$
87387
Linear equations given by $Ax = b$ have a solution if and only if $\operatorname{rank}(A|b) = \operatorname{rank}(A)$
71151
If $a_{ij}=\max(i,j)$, calculate the determinant of $A$
67058
Prove that $\text{rank}(X^TX)=\text{rank}(X)$
82591
Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.
70528
Rank of a Matrix Sum
83049
Frobenius Inequality Rank
19203
Is the rank of a matrix the same of its transpose? If yes, how can I prove it?
149287
Prove that $A,B>0$ and $A_{ij}0$