New posts in hermitian-matrices

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?

matrices hermitian-matrices

how to show that $A=[a_i+a_j]_{ij}$ has exactly one positive and one negative eigenvalue.

matrices hermitian-matrices

How to show that $(Re\lambda_1,\dotsb,Re\lambda_n)^T$ is majorized by $(\lambda_1(H),\dotsb,\lambda_n(H))^T$?

matrices hermitian-matrices

Minimal spanning set ("conical basis") for 2x2 Hermitian PSD (positive semi-definite) cone?

linear-algebra convex-analysis positive-semidefinite convex-cone hermitian-matrices

Can we construct an ORTHOGONAL ($trace(A^\dagger B) = 0$) basis for Hermitian matrices made of PSD (positive semi-definite) Hermitian matrices?

trace positive-semidefinite quantum-computation hermitian-matrices quantum-information

Can a symmetric matrix become non-symmetric by changing the basis?

linear-algebra matrices symmetric-matrices hermitian-matrices

Upper bound on norm of Hermitian matrix

linear-algebra matrices matrix-norms hermitian-matrices

What is a basis for the space of $n\times n$ Hermitian matrices?

linear-algebra matrices vector-spaces hermitian-matrices

Prove that Hermitian matrices are diagonalizable

linear-algebra matrices eigenvalues-eigenvectors diagonalization hermitian-matrices

Positive definite matrix must be Hermitian

linear-algebra matrices positive-definite hermitian-matrices

Properties of zero-diagonal symmetric matrices

linear-algebra matrices symmetric-matrices hermitian-matrices

A normal matrix with real eigenvalues is Hermitian

linear-algebra matrices eigenvalues-eigenvectors matrix-decomposition hermitian-matrices

Matrices which are both unitary and Hermitian

linear-algebra matrices unitary-matrices hermitian-matrices

Intuitive explanation of a positive semidefinite matrix

linear-algebra matrices intuition positive-semidefinite hermitian-matrices

How does one prove the determinant inequality $\det\left(6(A^3+B^3+C^3)+I_{n}\right)\ge 5^n\det(A^2+B^2+C^2)$?

linear-algebra matrices inequality determinant hermitian-matrices