Definition:Matrix/Square Matrix

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An $n \times n$ matrix is called a square matrix.

That is, a square matrix is a matrix which has the same number of rows as it has columns.

A square matrix is usually denoted $\sqbrk a_n$ in preference to $\sqbrk a_{n n}$.

Rectangular Matrix

A matrix which is specifically not a square matrix can be referred to as a rectangular matrix.

Order of Square Matrix

Let $\mathbf A$ be an $n \times n$ square matrix.

That is, let $\mathbf A$ have $n$ rows (and by definition $n$ columns).

Then the order of $\mathbf A$ is defined as being $n$.


Real $2 \times 2$ Square Matrix

A $2 \times 2$ real square matrix is an array of $4$ real numbers $p, q, r, s$ arranged as:

$\quad \mathbf A = \begin {bmatrix} p & q \\ r & s \end {bmatrix}$

$3 \times 3$ Square Matrix

The $3 \times 3$ square matrix is as follows:

$\quad \mathbf A = \begin {bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \\ \end {bmatrix}$

Also see

  • Results about square matrices can be found here.