# 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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### Is this “semi-tensor product” something recently invented? Are there other usages of it?

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### Eigenvalues of a block matrix with zero diagonal blocks

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### Routh-Hurwitz criterion for matrices

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### Operator norm of difference of matrix decompositions

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### Uniform continuity of Cholesky decomposition

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### Kulkarni-Nomizu square root of the Riemann tensor

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### System of matrix equations

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### When does a matrix subspace contain a full rank matrix?

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### Existence of matrices in the field $\mathbb{F}_2$ with some invertibility properties

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### Existence of a matrix in $\mathbb{F}_2$ with some invertibility properties

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### Upper bound on the sum of the smallest non-zero eigenvalues

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### Does there always exist a(n uniform) polynomial that makes a positive definite symmetric matrix with polynomial entries into a sum of squares?

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### Expressing a polynomial as the determinant of a matrix of linear forms

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### For which sets of linearly independent complex matrices does there exist a vector whose image set under the given matrices is linearly independent?

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### Spectral theorem for symmetric real tensors

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### Is it possible to reduce eigenvalues of tensors to an matrix eigenvalue problem?

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### Distribution and expectation of inverse of a random Bernoulli matrix

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### Rank of $A\otimes B - B\otimes A$

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### How to see that the determinant of this matrix is nonzero for all primes?

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### How many non-isomorphic associative algebras of dimension 2 over the field F_{p^k} are there?

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### Infinite positive matrices with probability eigenvector

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### General Sylvester's linear matrix equation

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### Which matrix decompositions feature permutation matrices?

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### How to compute an indefinite generalisation of QR decomposition

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### If $x \ge 0$ and $\mathbf{1}^Tx \le \|x\|^2$ then $\mathbf{1}^T(I - xx^T / \|x\|^2) \mathbf{1} \ge \| [\mathbf{1} - x]_+ \|^2$

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### Does there exist an O(n^3) algorithm for deciding whether PAP^T = LDU is solvable given some square matrix A?

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### Polynomiality of the inverse of equally weighted Varchenko matrices attached to hyperplane arrangements

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### For the purposes of solving linear equations, is there a fast decomposition that works for all Hermitian matrices?

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### Are there any results in generalizing matrix theory to multidimensional arrays? [closed]

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### Solving a Lyapunov inequality with a fixed block

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### Characteristic polynomial of a matrix related to pairs of elements generating $\mathbb{Z}/n\mathbb{Z}$

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### On the dimension of the projected rank $r$ matrix space

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### Symmetric matrices of hyperbolic and elliptic type with certain kind of trace zero

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### A lower-bound on matrix-function with vector product

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### Expectation of random matrix (minimum positive eigenvalue)

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### Determine unknown matrix function of particular form from known points

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### Projection onto column space perturbed by Gaussian noise

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### How to find the similarity transformation of a matrix operator?

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### Properties of matrix $X=\left[\frac{1}{1-\bar\alpha_i \alpha_j}\right]_{ij}$

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### Closed form solution for $XAX^{T}=B$

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### Derivative of matrix argument function with respect to eigenvalues of argument

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### A question of invertibility of matrices

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### How to adjust two Gramian matrices to make them “aligned” without enumeration?

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### Schrodinger operator with matrix potential

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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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