# 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.

**237**

**25**answers

### Geometric Interpretation of Trace

**87**

**9**answers

### Should the formula for the inverse of a 2x2 matrix be obvious?

**71**

**3**answers

### Norms of Commutators

**56**

**7**answers

### How to prove this determinant is positive?

**55**

**1**answer

### Geometric interpretation of characteristic polynomial

**51**

**4**answers

### Eigenvalues of matrix sums

**48**

**1**answer

### Invertible matrices over noncommutative rings

**44**

**1**answer

### Determinant of a determinant

**38**

**3**answers

### The probability for a symmetric matrix to be positive definite

**36**

**6**answers

### Determinant of sum of positive definite matrices

**35**

**3**answers

### A curious determinantal inequality

**33**

**2**answers

### How fast can we *really* multiply matrices?

**30**

**7**answers

### Does the truth of any statement of real matrix algebra stabilize in sufficiently high dimensions?

**29**

**3**answers

### Perron-Frobenius “inverse eigenvalue problem”

**28**

**4**answers

### Adjacency matrices of graphs

**27**

**12**answers

### When does 'positive' imply 'sum of squares'?

**27**

**1**answer

### Is there an explicit formula for the hessian of “Determinant”?

**27**

**1**answer

### Properties to have matrices that commute in $\mathrm{GL}_n(\mathbb C)$

**27**

**2**answers

### Invertible matrices satisfying $[x,y,y]=x$

**27**

**1**answer

### Understanding “infinite” relations in groups

**26**

**10**answers

### When to pick a basis?

**26**

**4**answers

### Matrices: characterizing pairs $(AB, BA)$

**26**

**0**answers

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

**25**

**1**answer

### Determinants of binary matrices

**25**

**2**answers

### Symmetric strengthening of the Cauchy-Schwarz inequality

**24**

**5**answers

### When is a matrix power nonnegative

**24**

**2**answers

### Is this proof of Perron's theorem correct, and if so is it original?

**24**

**2**answers

### Factorization of a real matrix into Hermitian x Hermitian. Is it stable ?

**24**

**0**answers

### Real square roots of symmetric matrices

**23**

**3**answers

### On determinants formed by binomial coefficients

**23**

**3**answers

### Is every positive integer the permanent of some 0-1 matrix?

**23**

**2**answers

### Finite subgroups of unitary groups

**22**

**6**answers

### Expressing adj(A) as a polynomial in A?

**22**

**6**answers

### Cayley-Hamilton revisited

**22**

**5**answers

### Deriving inverse of Hilbert matrix

**22**

**2**answers

### Infinite matrices and the concept of “determinant”

**21**

**1**answer

### maximal order of elements in GL(n,p)

**21**

**6**answers

### What are the possible eigenvalues of these matrices?

**21**

**4**answers

### A matrix algebra has no deformations?

**21**

**2**answers

### Singular values of sequence of growing matrices

**21**

**4**answers

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

**21**

**0**answers

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

**21**

**0**answers

### The Fourier Transform of taking Eigenvalues

**20**

**6**answers

### how to find/define eigenvectors as a continuous function of matrix?

**20**

**4**answers

### Does Anyone Know Anything about the Determinant and/or Inverse of this Matrix?

**20**

**2**answers

### Integer matrices with no integer eigenvalues

**20**

**2**answers

### Lifting matrices mod 2 to integers.

**20**

**3**answers

### Simultaneous “orthonormalization” in $\mathbb{C}^4$

**20**

**0**answers

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

**20**

**0**answers