# 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 [tag: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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### Sparse dense matrix versus Non-sparse dense matrix in eigenvalue computation

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### How to find the best similarity transformation between two symmetric matrices $\mathbf{A}$ and $\mathbf{B}$?

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### How to show that a continuous family of symmetric matrices is uniformly positive?

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### Matrix Product Chain Representation of an Addition Chain [closed]

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### Existence of orthogonal basis of symmetric $n\times n$ matrices, where each matrix is unitary?

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### Computing with a vector subspace equipped with a prescribed basis over finite fields

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### Decide if a matrix is transposable

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### Largest eigenvalues of a (random) correlation matrix?

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### How to compute inverse of sum of a unitary matrix and a full rank diagonal matrix?

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### non-backtracking random walk in regular (finite) graphs

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### Is every stable matrix orthogonally similar to a $D$-skew-symmetric matrix?

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### The determinant of a $4\times4$ matrix associated to some specific polynomial as follow

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### Existence of an “almost” skew-symmetric matrix

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### On the existence of integer square root of a $3 \times 3$ positive definite matrix

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### On a matrix inequality based on the Schur-Horn theorem

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### A (linear) optimization problem subject to (linear) matrix inequality constraints

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### Calculate the rank of a symmetric matrix

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### A “positive diagonal plus skew-symmetric” matrix decomposition

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### eigenvalues of a square block matrix

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### A parametrization of stable matrices

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### Is the linear span of special orthogonal matrices equal to the whole space of $N\times N$ matrices?

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### Bounds of Procrustes problem

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### About product of PSD matrices

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### Matrix Bernstein for spherical random variables

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### Clebsch–Gordan decomposition for $\mathrm{SU}(2)$, in indices

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### Derivative of complex matrix pseudo inverse with respect to real and imaginary components

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### find linear approximation of non-linear matrix transform [closed]

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### Characterizing a subclass of row-orthogonal matrices

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### On ranks of matrices with tensor structure

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### Generalizing Autonne-Takagi factorization

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### Connections between eigenvectors after matrix multiplication

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### On a condition for a matrix sum to be zero

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### Square root of a large sparse symmetric positive definite matrix

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### An upper bound on the Jordan condition number of a matrix

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### Classifications of the indefinite generalized Cartan matrix

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### Well known matrix inequality?

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### Differentiability of Eigenvalues - Perturbation Theory

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### Is it hard to decide whether a matrix is a square of another matrix?

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### Finding an adjacency matrix whose cube's diagonal is equal to a given vector

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### Nuclear norm as minimum of Frobenius norm product

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### A variant of Specht's Theorem using sum of elements (rather than trace) of complex matrices?

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### An inequality regarding projection

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### Expected value of determinant of simple infinite random matrix

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### Is there a usual technical term for this set-valued function associated to a zero-one matrix?

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### Regarding minimal elementary generators for $GL(n, \mathbb{Z})$

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### Matrix continued fractions

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### Lower bounds on eigenvalues of Lyapunov solutions

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### A Handbook of Matrix Factorizations

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### Eigenvalues and eigenvectors of tridiagonal matrices

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