New posts in matrix-rank

If $\rho\leq\sigma$, is $\operatorname{rank}(\rho)\leq\operatorname{rank}(\sigma)$?

linear-algebra matrix-rank positive-semidefinite

Can symmetric rank two matrices be written as $WW^{\top}$?

linear-algebra matrix-rank symmetric-matrices

Why do elementary matrix operations not affect the row space of a given matrix?

linear-algebra matrix-rank

Rank of the $n \times n$ matrix with ones on the main diagonal and $a$ off the main diagonal

linear-algebra matrices matrix-rank symmetric-matrices

Intuition & Proof of rank(AB) $\le$ min{rank(A), rank(B)} (without inverses or maps) [Poole P217 3.6.59, 60]

linear-algebra matrices intuition matrix-rank visualization

Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$

linear-algebra matrices proof-verification matrix-rank

Expected rank of a random binary matrix?

probability matrices reference-request matrix-rank random-matrices

Let $A$ be a $n\times n$ matrix with entries $a_{ij}=i+j $ . Calculate rank of $A$

linear-algebra abstract-algebra matrices matrix-rank

If $AB=0$ prove that $\mathrm{rank}(A)+\mathrm{rank}(B)\leq n$

matrices inequality matrix-rank

A rank-one matrix is the product of two vectors

linear-algebra matrices vector-spaces matrix-rank transpose

Prove Sylvester rank inequality: $\text{rank}(AB)\ge\text{rank}(A)+\text{rank}(B)-n$

linear-algebra matrices inequality contest-math matrix-rank

Why is minimizing the nuclear norm of a matrix a good surrogate for minimizing the rank?

linear-algebra matrices normed-spaces matrix-rank nuclear-norm

Rank of a $n! \times n$ matrix

linear-algebra matrices matrix-rank

Proof that determinant rank equals row/column rank

linear-algebra matrix-rank

Proof that the rank of a skew-symmetric matrix is at least $2$

linear-algebra matrices matrix-rank skew-symmetric-matrices

How to determine $\mathrm{rank}(p(A))$ if you know the rational canonical form of $A$

linear-algebra matrix-rank

Is the rank of a matrix the same of its transpose? If yes, how can I prove it?

linear-algebra matrices matrix-rank transpose

What is the relation between rank of a matrix, its eigenvalues and eigenvectors

linear-algebra eigenvalues-eigenvectors matrix-rank

Sylvester rank inequality: $\operatorname{rank} A + \operatorname{rank}B \leq \operatorname{rank} AB + n$ [duplicate]

linear-algebra matrices inequality matrix-rank

Show $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A+B)$

linear-algebra matrices inequality matrix-rank