# Questions tagged [matrix-theory]

Matrix theory is the study of matrices as concrete objects, rather than as abstract linear operators between vector spaces (whose study belongs to linear algebra). For instance, this involves matrix factorizations and decompositions, nonnegative matrices and Perron-Frobenius theory, Schur complements, structured and special matrices, matrix functions and equations.

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### Schrodinger operator with matrix potential

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### Schaten p norm of block matrices

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### Find occurrences of certain matrix inside a matrix

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### Bound for matrix inner product based on singular values

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### Upper and lower bounds on the entries of a matrix power

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### Inequality for $AB + BA$ when $A,B\geq0$, reference request

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### Minimum rank of a product of two block diagonal matrices with an arbitrary matrix

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### Random sparse and invertible matrices

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### A system of inequalities involving a skew-symmetric integer matrix

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### Minimum of $\mathrm{rank}\left( \boldsymbol{W} \boldsymbol{H} \right)$, with $\boldsymbol{W}$ block diagonal

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### Convergence rate of Toda/Morse flow

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### Minors of low rank skew-symmetric matrix

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### Matrix Lie algebra: Semisimple element = semisimple matrix?

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### Joint convexity of trace of matrices

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### Update rank-revealing factorization after applying $I \otimes $(small matrix)

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### Spectral abscissa of symmetric matrix with skew-symmetric perturbation

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### Representation theorem for matrices (reference request)

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### Spectral norm bound on smooth primary matrix function perturbation

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### Eigenvalues of product of symmetric positive definite matrices

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### Choosing the best submatrix

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### LU decomposition for orthogonal or unitary matrices?

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### Eigenvalues of the matrix obtained by letting some of the rows vanish, hoping for some inequality

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### What are known properties of matrices where off-diagonal elements are 1?

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### On norm convergence of a commutator and implications

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### Are unitarily equivalent permutation matrices permutation similar?

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### Can I assign the term “is eigenvector” and “is eigenmatrix” of matrix **P** in my specific (infinite-size) case?

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### Matrix equations motivated by generalization of $QR$ decomposition

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### Eigenvectors of Kronecker Product [closed]

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### Nullity of infinite matrix in row echelon form

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### Symmetrization of pentadiagonal matrices

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### Is every finite-order unimodular matrix conjugate to a $0,1,-1$ matrix?

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### Consequences of eigenvector-eigenvalue formula found by studying neutrinos

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### Transformations preserving the number of distinct eigenvalues

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### Controlling the rank of a Matrix product

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### Existence of solution for system of quadratic equations

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### How to derive the mean of inverse-Wishart distribution?

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### What is the expected inverse of 1 plus a Wishart distribution?

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### How wide is the Birkhoff Polytope?

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### Homotopicity of $a\mapsto a\otimes 1$ and $a \mapsto 1\otimes a$ as morphisms from $A$ to $A\otimes A$

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### Quantum inspired matrix inequality

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### Row-based iterative algorithms for computing the kernel of a matrix

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### Checking a matrix for distinct rows

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### Differentiability of operator norm [closed]

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### Conjugation of Irreducible {0,1}-Matrices by Orthogonal Matrix

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### Coloring in Combinatorial Design Generalizing Latin Square

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### Additivity of the Field of Values

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### Frobenius normal form of a doubly stochastic matrix

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### Jordan Decomposition of Sparse matrix

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### Best orthogonal approximation of rank 1 matrix

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