# 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.

**3**

**0**answers

### Is every matrix involution over a UFD diagonalisable?

**0**

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### How to prove the Ky Fan inequality and its opposite

**0**

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### Low-discrepancy submatrices in any matrix

**0**

**0**answers

### Lagrange Optimization w.r.t. vector + equality constraint

**1**

**1**answer

### Weak majorizations for sum of two hermitian matrices

**4**

**1**answer

### The largest $\ell_p$-norm of a sum of rows of a Sylvester-Hadamard-Walsh matrix

**2**

**1**answer

### Monotonicity of the determinant of symmetric Toeplitz Matrices

**11**

**2**answers

### The character table of the symmetric group modulo m

**8**

**2**answers

### $2$-norm of idempotent matrix

**0**

**0**answers

### Derivative of a hermitian matrix of power $n$ by a scalar [closed]

**3**

**1**answer

### Derivative of an integral of a Gaussian

**8**

**1**answer

### For every ring R, is there a block-diagonal canonical form for a square matrix over R?

**5**

**1**answer

### Combinatorics and symmetry in matrices under row and column swaps

**3**

**2**answers

### Relation graph isomorphism to discrete logarithm

**2**

**0**answers

### Finding a basis for the range of a linear function

**1**

**0**answers

### Convolution integral and its matrix representation

**2**

**0**answers

### Intuition behind eigenvalues of a graph mattering

**1**

**1**answer

### Condition on the probabilities for the $J\times J$ matrix $[ \Pr(X=j \mid Y=k) ]$ to be invertible

**5**

**0**answers

### Matrix decompositions as monoid isomorphisms. Ever considered before?

**2**

**0**answers

### The "matrix direct sum" monoid modulo unitary equivalence

**2**

**1**answer

### Is the number of values the sign function can take on a ring ("signedness") of any fundamental importance? Can it be predicted?

**1**

**0**answers

### Largest eigenvalue of matrix A smaller than 1, what about B when A=B+C? [closed]

**5**

**2**answers

### Sorting energy bands in physics

**1**

**0**answers

### There is an observation on the eigenvalues of the sum of a kind of special Hermitian matrices. How to prove it?

**0**

**0**answers

### Is the kernel $\vert d_X - d_Y \vert^p$ conditionally negative definite?

**0**

**0**answers

### Improving a basis

**12**

**4**answers

### Show that the eigenvalues of a non-symmetric matrix built from positive matrices have positive real parts

**0**

**0**answers

### Expressing a diagonal matrix over a division ring

**1**

**1**answer

### $C\lVert\sum_i a_{ii}\rVert \ge \lVert(a_{ij})\rVert$ for matrices with entries in a $C^*$-algebra

**1**

**0**answers

### Positive semidefinite fundamental solution to Schrodinger operator

**2**

**0**answers

### Product of two involutions in $\mathrm{PSL}_2(D)$

**0**

**1**answer

### Does there exist a function $f(X)$ with the following gradient $\mathrm{Tr}[(I-X)^{-1}]\cdot g(X)$?

**7**

**1**answer

### Is it true that $\lVert A\rVert \leq \lVert A^2\rVert$ for $A\in \operatorname{SL}(2, \mathbb{R})$ when $\operatorname{trace}(A)>2$?

**0**

**1**answer

### Product of matrices equal identity

**16**

**1**answer

### Uniquely reconstruct a matrix $M$ from its inverse $M^{-1}$ if $n$ elements of $M^{-1}$ are unknown and $n$ elements of $M$ are given

**7**

**2**answers

### Finding a matrix from its diagonal and the off-diagonal elements of its inverse?

**1**

**1**answer

### Combinatorial graph optimization problem on integer adjacency matrices

**2**

**2**answers

### When is $(I - X)^{-\top} \circ X = 0$?

**1**

**1**answer

### Upper bound of rank of a matrix

**1**

**0**answers

### How to fill a rectangle with smaller rectangles of given sizes?

**5**

**1**answer

### Convergence of a series related to $\mathrm{SL}_2({\mathbb N})$

**0**

**1**answer

### The eigenvectors and eigenvalues of Laplacian matrix in a chain graph

**4**

**2**answers

### Computation of the pfaffian of a particular matrix

**1**

**0**answers

### Trace minimization for generalized eigenvalue problem

**1**

**1**answer

### Matrix equation with projection matrix

**1**

**0**answers

### Derivative of a function of ordered variables

**-5**

**1**answer

### Can we say that everywhere where it makes sense $\log_0 x=0^x$? Are they equal, the function is self-inverse? If so, what is deep intuition behind it? [closed]

**2**

**1**answer

### Existence of matrices with some invertibility properties

**2**

**0**answers

### For a nilpotent matrix A, are the cardinalities of sets: 1) B: commute with A, 2) B: anticommute with A, 3) B: q-commute with A — the same?

**0**

**2**answers