Questions tagged [matrices]

For any topic related to matrices. This includes: systems of linear equations, eigenvalues and eigenvectors (diagonalization, triangularization), determinant, trace, characteristic polynomial, adjugate and adjoint, transpose, Jordan normal form, matrix algorithms (e.g. LU, Gauss elimination, SVD, QR), invariant factors, quadratic forms, etc. For questions specifically concerning matrix equations, use the (matrix-equations) tag.

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7
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1answer
191 views
+100

Representing the determinant of a Hermitian matrix as an integral

Let $M=\left (\omega\mathbb{I}-A\right )\left(\omega^{*}\mathbb{I}-A^{\dagger}\right)$ be a Hermitian matrix of size $n\times n$ where $A$ is a real non symmetric matrix and $\omega=a+\mathrm{i}b$. $A^...
7
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2answers
105 views
+50

Every matrix of the centralizer of the centralizer of a matrix is a polynomial in that matrix

Let $V=M(n,\mathbb C)$. For a subset $S \subseteq V$, let $C(S):=\{A \in V | AB=BA, \forall B \in S \}$ . How to prove that for every $A\in V$, we have $C(C (\{A\})) \subseteq \{ p(A) | p(t) \in \...