# Questions tagged [matrices]

Questions where the notion matrix has an important or crucial role (for the latter, note the tag matrix-theory for potential use). Matrices appear in various parts of mathematics, and this tag is typically combined with other tags to make the general subject clear, such as an appropriate top-level tag ra.rings-and-algebras, co.combinatorics, etc. and other tags that might be applicable. There are also several more specialized tags concerning matrices.

**26**

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

**24**

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### Real square roots of symmetric matrices

**21**

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### Noncommutative arithmetic mean geometric mean inequality and symmetric polynomials

**21**

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### The Fourier Transform of taking Eigenvalues

**20**

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### An $n \times n$ matrix $A$ is similar to its transpose $A^{\top}$: elementary proof?

**20**

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### Cauchy matrices with elementary symmetric polynomials

**19**

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### “quantum” symmetric plane partitions beget alternating sign matrices?

**16**

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### How boundedly generated is $SL_3(\mathbb{Z})$?

**15**

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### An inequality for matrix norms

**15**

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### When is the determinant an $8$-th power?

**15**

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### Determinant inequality involving Hermitian, positive definite matrices

**14**

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### The rank of a “triangle-free” matrix

**14**

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### Is “being a full ring of quotients” a Morita invariant property?

**13**

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### Descartes rule of signs for a noncommutative polynomial in matrix variables

**13**

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### Diagonalizing some matrices arising from Fourier transform on $S_n$.

**12**

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### Pointwise (Hadamard) matrix product and the rank

**12**

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### Which ordering of factors is needed to obtain this kind of determinantal inequalities?

**12**

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### Ratio of entries of A and log A where A is a triangular matrix

**12**

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### Eigenvalues of permutations of a real matrix: how complex can they be?

**12**

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### Regular languages of matrices and their generating functions

**11**

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### Matrices that admit a power that is symmetric

**11**

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### Fast computation of matrix product $AXA^T$ with fixed $A$?

**11**

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### Jaffard's theorem - finite matrices

**11**

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### Is my matrix perturbation analysis legitimate?

**11**

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### Generalized Classical Adjoints and Factorizations of the Characteristic Polynomial

**10**

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### What are these matrices called?

**10**

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### Poset of nonvanishing minors of a matrix

**10**

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### Matrix identities in two variables

**10**

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### A $k \times n$ matrix with a lot of invertible $k \times k$ submatrices over $\mathbb{F}_2$

**10**

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### Determining the kernel of a Vandermonde-like matrix

**9**

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### Comparison of the absolute value of an operator with its positive parts, II

**9**

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### Eigenvalues of leading principal submatrix of the Clement-Kac-Sylvester tridiagonal matrix

**9**

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### Rationality of a certain real algebraic variety

**9**

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### Is there any study about positive definiteness of some matrix space whose matrices don't have to be positive-definite?

**8**

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### Nonzero subdeterminants conjecture: has anybody seen this anywhere?

**8**

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### Solving matrix equation $X^{-1}=\sum_{i=1}^n D_i X A_i$

**8**

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### Name for an operation on matrices?

**8**

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### Finding $U,V$ in Thompson's Formula

**8**

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### Bounding sum of first singular values squared for Kronecker sum of traceless matrices

**8**

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### Path connected set of matrices?

**8**

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### Standard polynomials applied to matrices (bis)

**7**

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### A limiting sequence of positive definite matrices

**7**

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### A generalization of matrix minors to non-integer values

**7**

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### Bound on gap between least eigenvalues of $n \times n$ correlation matrix and of its $(n -1) \times (n-1)$ submatrices

**7**

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### Counting 0-1 $n\times n$ matrices with a given rank r

**7**

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### A special eigenvalue problem

**7**

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### Quantum coupon collection: positivity of an alternating sum of matrices

**7**

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### A conjecture of Lubotzky on ranks of subgroups of special linear groups over the integers

**7**

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### Does $\varphi: \mathbb{P}^{n} \to \mathbb{P}^{n}$ have periodic points missing the critical hypersurface?

**7**

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