PlanetMath: square matrix

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square matrix

(Definition)

A square matrix has the same number of rows as columns.

Examples:

$\begin{pmatrix} 1.00000 & 0.50000 & 0.33333 & 0.25000 \ 0.50000 & 0.33333 & ... ...00 & 0.20000 & 0.16667 \ 0.25000 & 0.20000 & 0.16667 & 0.14286 \end{pmatrix}$
$\begin{pmatrix}1\end{pmatrix}$
$\begin{pmatrix} 0.94 & 0.37 & 0.71 & 0.32 & 0.58 \ 0.90 & 0.16 & 0.74 & 0.83... ... & 0.59 & 0.43 & 0.03 & 0.76 \ 0.04 & 0.64 & 0.61 & 0.17 & 0.29 \end{pmatrix}$
$\begin{pmatrix}89 & 38 & 50 \\ 64 & 26 & 98 \\ 40 & 96 & 83 \end{pmatrix}$

The notation $\operatorname{Mat}_n(\mathbb{K})$ is often used to signify the set of square matrices which are of order (size $n \times n$ ) with elements drawn from a field $\mathbb{K}$ . Thus, one would use $a \in \operatorname{Mat}_3(\mathbb{C})$ to declare that is a three-by-three matrix with elements that are complex numbers.

Property: Suppose and are matrices such that is a square matrix. Then the product is defined and also a square matrix.

"square matrix" is owned by akrowne.

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Cross-references: product, property, complex numbers, matrix, field, size, order, columns, rows
There are 76 references to this entry.

This is version 5 of square matrix, born on 2002-01-13, modified 2006-08-02.
Object id is 1472, canonical name is SquareMatrix.
Accessed 12666 times total.

Classification:

AMS MSC:

15-00 (Linear and multilinear algebra; matrix theory :: General reference works )

Pending Errata and Addenda

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