# 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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### How to solve linear system of form $(A \otimes B + C^{T}C)x = b$ when $A \otimes B$ is too large to compute?

For the given linear system: $$(A \otimes B + C^{T}C)x = b$$ where $\otimes$ is the Kronecker product, $A$ and $B$ are dense and symmetric positive-definite, and $C^{T}C$ is a sparse symmetric block ...
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### Can the Riemann hypothesis be relaxed to say that this matrix A consists of square roots?

I realize that asking this question is like presenting to a patent attorney a wheel-less skateboard while asking to patent a hoverboard. Anyways. Lagarias version of the Riemann hypothesis sets a ...
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### Number of n X n binary matrices with every 1 adjacent to some zero and every 0 adjacent to some one, horizontally or vertically.

I came across this integer sequence: A133792. It represents the number of $n\times n$ binary matrices with every 1 adjacent to some zero and every 0 adjacent to some one, horizontally or vertically. ...
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### Triangularization of matrix over PID

Let $R$ be a PID and let $A \in Mat_n(R)$ with all of its eigenvalues in R. Is it true that I can always find $P \in GL_n(R)$ such that $P^{-1}AP$ is uppertriangular? If so can I have a reference ...
### A Matrix Norm Inequality $\|A^{1/2}B^{1/2}(A+B)^{-1/2}\|_F \geq \|A^{1/2}(A+B)^{-1/2}B^{1/2}\|_F$
Let $\|X\|_F:= \sqrt{\text{Tr} \left(XX^\dagger\right) }$ denote the Frobenius norm. Does anyone know how to show the norm inequality: \$\left\|A^{\frac12}B^{\frac12}(A+B)^{-\frac12}\right\|_F \geq ...