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Generation of Hermitian invertible matrix with fixed number of non-zero elements

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#linear-algebra #eigenvalues-eigenvectors #unitary-matrices #hermitian-matrices
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Inequalities on the trace of matrix products

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#inequality #trace #unitary-matrices #hermitian-matrices
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Can a symmetric matrix become non-symmetric by changing the basis?

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#linear-algebra #matrices #symmetric-matrices #hermitian-matrices
199
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Diagonalising an infinite-dimensional Hermitian square matrix

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#matrices #mathematical-physics #diagonalization #quantum-mechanics #hermitian-matrices
223
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Find a matrix $B$ such that $B^* B=A$ for a given Hermitian $A$

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#linear-algebra #matrices #hermitian-matrices
3.8k
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$A^2=A^*A$. Why is matrix $A$ Hermitian?

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#linear-algebra #matrices #hermitian-matrices
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Is it possible to find a companion matrix of a polynomial which is also hermitian?

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#linear-algebra #matrices #eigenvalues-eigenvectors #hermitian-matrices #companion-matrices
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Diagonal matrix is normal

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#linear-algebra #matrices #complex-numbers #hermitian-matrices
121
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$A, B, C$ hermitian matrix and $C \geq 0, A \leq B$. Then, $tr(CA) \leq tr(CB)$

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#matrices #inequality #trace #hermitian-matrices
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Hermitian matrix has positive eigenvalues

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#linear-algebra #matrices #eigenvalues-eigenvectors #hermitian-matrices
13.6k
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Show that the set of Hermitian matrices forms a real vector space

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#linear-algebra #matrices #vector-spaces #hermitian-matrices
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Prove the following result for Hermitian and Skew-Hermitian matrix

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#matrices #hermitian-matrices
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Prove that Hermitian matrices are diagonalizable

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#linear-algebra #matrices #eigenvalues-eigenvectors #diagonalization #hermitian-matrices
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Hermitian Matrix

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#matrices #vector-spaces #hermitian-matrices
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Convert Hermitian matrix to symmetric

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#matrices #transformation #symmetric-matrices #hermitian-matrices

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