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# 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.

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### Number of matrices with bounded products of rows and columns

Fix an integer $d \geq 2$ and for every real number $x$ let $M_d(x)$ be number of $d \times d$ matrices $(a_{ij})$ satisfying: every $a_{ij}$ is a positive integer, the product of every row does not ...
1answer
186 views

### Inequality involving tensor product of orthonormal unit vectors

Let $e_1,...,e_r$ be the first $r$ standard basis of $\mathbb{R}^n, r<n$. Let $u_1,...,u_n$ be another orthonormal basis of $\mathbb{R}^n$. Let $\otimes$ be the tensor product on $\mathbb{R}^n$ and ...
0answers
121 views

### Is there literature on the study of “eigenmatrices”?

Starting with a disclaimer: I will not be able to describe this with the correct terminology because I am trying to find the literature which I am unsure of it's existence. I will try to explain what ...
1answer
42 views

### Rank and edges in a combinatorial graph?

Fix a $d\in\mathbb N$ and consider the matrix $M\in\{0,1\}^{2^d\times d}$ of all $0/1$ vectors of length $d$. Consider the matrix $G\in\{0,1\}^{n\times n}$ whose $ij$ the entry is $0$ if inner product ...
0answers
54 views

### Approximate inverse of large sparse matrix

Given a large sparse matrix $M$, how to determine the existence of a good preconditioner? In other words, does there exist a sparse matrix $X$ such that $X M$ is close to the identity with respect to ...
0answers
31 views

2answers
164 views

### $2$-norm distance between square roots of matrices

Suppose two square real matrices $A$ and $B$ are close in the Schatten 1-norm, i.e. $\|A-B\|_1=\varepsilon$. Can this be used to put a bound on the Schatten 2-norm distance between their square roots. ...
0answers
126 views

### A combinatorial / geometric interpretation of compositional inversion via matrix inversion

There are several ways of finding the power or Taylor series for the compositional inverse of a function $f(x)$ with $f(0)=0\;$ given its series expansion, e.g., by using the classic Lagrange ...
1answer
66 views

### Energy of a symmetric matrix with $0$, $1$ or $-1$ entries

I have a symmetric matrix with entries $0$, $1$ or $-1$ which appeared in my works in graph theory (the diagonal entries are all zero). I need a good upper bound for the energy of this matrix; i.e. "...

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