Newbetuts

Dimension of a Subspace of $\text{Hom}_\mathbb{K}(\mathcal{V},\mathcal{W})$ Consisting of Only Linear Transformations of Rank $\leq r$

Eigenvalue bound for quadratic maximization with linear constraint

Prove that all nxn nilpotent matrices of order n are similar.

Finding rotation of 3 given lines in 3D until intersection with 3 other given lines

How many matrices exist with this increasing row and increasing column condition?

Positive semidefiniteness of a block matrix of positive semidefinite matrices

$n \times n$ matrix whose entries $\in \{1,2\}$, such that $7$ divides the sum of every column and $5$ divides the sum of every row

Regarding trace of idempotent matrix multiplied by its transpose

If $A \in M_{n,n}(\mathbb F)$ is invertible then $A = UPB$, $U$ is unipotent upper triangular, $B$ is upper triangular and $P$ is a permutation.

For $T\in \mathcal L(V)$, we have $\text{adj}(T)T=(\det T)I$.

Prove that, at least one of the matrices $A+B$ and $A-B$ has to be singular

Eigenvalues of inverse matrix to a given matrix

$\operatorname{rank}(A^2)+\operatorname{rank}(B^2)\geq2\operatorname{rank}(AB)$ whenever $AB=BA$?

Did I just discover a new way to calculate the signature of a matrix?

Given a square matrix $A$, both $AA^T$ and $A^TA$ are symmetric

If $A,B$ are Hermitian, how to show that $\lambda_\max(AB^{-1}) =\max_{x\ne 0} \frac{x^Ax}{x^Bx}$ if A,B have only positive eigenvalues?

Finding Euler decomposition of a symplectic matrix

New posts in matrices

Ensuring that a symmetric matrix with nonnegative elements is positive semidefinite

Are the eigenvectors of a real symmetric matrix always an orthonormal basis without change?

Sum of singular values of a matrix

Dimension of a Subspace of $\text{Hom}_\mathbb{K}(\mathcal{V},\mathcal{W})$ Consisting of Only Linear Transformations of Rank $\leq r$

Eigenvalue bound for quadratic maximization with linear constraint

Prove that all nxn nilpotent matrices of order n are similar.

Finding rotation of 3 given lines in 3D until intersection with 3 other given lines

How many matrices exist with this increasing row and increasing column condition?

Positive semidefiniteness of a block matrix of positive semidefinite matrices

$n \times n$ matrix whose entries $\in \{1,2\}$, such that $7$ divides the sum of every column and $5$ divides the sum of every row

Regarding trace of idempotent matrix multiplied by its transpose

If $A \in M_{n,n}(\mathbb F)$ is invertible then $A = UPB$, $U$ is unipotent upper triangular, $B$ is upper triangular and $P$ is a permutation.

For $T\in \mathcal L(V)$, we have $\text{adj}(T)T=(\det T)I$.

Prove that, at least one of the matrices $A+B$ and $A-B$ has to be singular

Eigenvalues of inverse matrix to a given matrix

$\operatorname{rank}(A^2)+\operatorname{rank}(B^2)\geq2\operatorname{rank}(AB)$ whenever $AB=BA$?

Did I just discover a new way to calculate the signature of a matrix?

Given a square matrix $A$, both $AA^T$ and $A^TA$ are symmetric

If $A,B$ are Hermitian, how to show that $\lambda_\max(AB^{-1}) =\max_{x\ne 0} \frac{x^Ax}{x^Bx}$ if A,B have only positive eigenvalues?

Finding Euler decomposition of a symplectic matrix