New posts in matrices

Show that trace is a unique linear functional

linear-algebra matrices trace

Second order approximation of log det X

matrices matrix-calculus hessian-matrix scalar-fields

degree of nilpotent matrix

linear-algebra matrices nilpotence

is it true every left inverse of a matrix is also right inverse of it?

linear-algebra matrices inverse

Is spectral radius = operator norm for a positive valued matrix?

matrices matrix-norms spectral-radius spectral-norm positive-matrices

Checking if a matrix is positive semidefinite

matrices positive-semidefinite

Finding the basis of $\mathfrak{so}(2,2)$ (Lie-Algebra of $SO(2,2)$)

matrices lie-groups lie-algebras matrix-equations

Is every invertible matrix a change of basis matrix?

linear-algebra matrices inverse

Compute the determinant of order n + 1 (n ≥ 2)

linear-algebra matrices determinant

Characteristic polynomial of the matrix with zeros on the diagonal and ones elsewhere

linear-algebra matrices

Why is the optimal solution to $ \min\limits_{S \in \mathbb S^{n}_{+}} -\log(\det(S))+\text{trace}(\Sigma S)$ equal to $\Sigma^{-1}$

real-analysis linear-algebra matrices optimization

If $A$ is a $n\times n$ matrix that satisfies $A^2=A$, then prove that $\operatorname{rank}(A)+\operatorname{rank}(I-A)=n$ [closed]

linear-algebra matrices

Why can a matrix without a full rank not be invertible?

linear-algebra matrices determinant

Can we say that the matrix $\begin{bmatrix} A & A \\ 0 & A \end{bmatrix}$ is diagonalizable if and only if $A = 0$?

linear-algebra matrices diagonalization

What are the eigenvalues of $A(A+I)^{-1}$ in terms of the eigenvalues of SPSD matrix $A$?

linear-algebra matrices eigenvalues-eigenvectors contraction-operator

How to test if a graph is fully connected and finding isolated graphs from an adjacency matrix

linear-algebra matrices graph-theory algorithms

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 $\det(AA^T)=nk^2.$

linear-algebra matrices

How to compute time ordered Exponential?

matrices ordinary-differential-equations multivariable-calculus exponential-function matrix-calculus

The Inverse of a Fourth Order Tensor

matrices multivariable-calculus mathematical-physics tensors

What are the $\succ$ and $\prec$ operators for when used with matrices?

matrices notation