# 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.

2,061 questions
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### Variation on a matrix game

The original problem appeared on last year's Putnam exam: "Alan and Barbara play a game in which they take turns filling entries of an initially empty 2008×2008 array. Alan plays ﬁrst. At each turn, ...
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### Surjective maps given by words, redux

I asked some time ago: Let $w(X,Y)$ be a word in $X$ and $Y$ (i.e., an element in the free group on $X$ and $Y$). Let the variables $x$ and $y$ now range among elements of $SL_n(K)$, $K$ an ...
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### Infinite matrices and the concept of “determinant”

Suppose we have an infinite matrix A = (aij) (i, j positive integers). What is the "right" definition of determinant of such a matrix? (Or does such a notion even exist?) Of course, I don't ...
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### Determinant of a pullback diagram

Suppose that X and Y are finite sets and that f : X → Y is an arbitrary map. Let PB denote the pullback of f with itself (in the category of sets) as displayed by the commutative diagram PB &...
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### What is the constant of the Coppersmith-Winograd matrix multiplication algorithm

Or at least it's order of magnitude. I've only ever heard it described as "huge", and a google search turned up nothing. Also, given that the Strassen algorithm has a significantly greater constant ...
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### Euclidean volume of the unit ball of matrices under the matrix norm

The matrix norm for an n-by-n matrix A is defined as |A|=max(|Ax|) where x ranges over all vectors with |x|=1, and the norm on the vectors in R^n is the usual Euclidean one. This is also called the ...
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### An “existence contra partition of unity” statement for integer matrices?

While reading a blog post on partitions of unity at the Secret Blogging Seminar the following question came into my mind. Let $n$ be a positive integer and let $B_1$ and $B_2$ be $n \times n$ ...
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### Linear transformation that preserves the determinant

It seems "common knowledge" that the following holds: Let $T$ be a linear transformation on nxn matrices with complex coefficients that preserves the determinant. Then there exists matrices U and V ...
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### Does the space of $n \times n$, positive-definite, self-adjoint, real matrices have a better name?

This is also the space of real, symmetric bilinear forms in $\Bbb R^n$.
Given a matrix equation $Ax=b$ where $A$ is a matrix and $b$ is a column vector, what is a condition that would ensure that there is a column vector $x$ that satisfies the equation? Assume the ...