Definition:Nonsingular Matrix/Definition 3

Definition

Let $\struct {R, +, \circ}$ be a ring with unity.

Let $n \in \Z_{>0}$ be a (strictly) positive integer.

Let $\mathbf A$ be an element of the ring of square matrices $\struct {\map {\MM_R} n, +, \times}$.

$\mathbf A$ is a nonsingular matrix if and only if $\mathbf A$ is not singular.

Also known as

Nonsingular matrix can also be seen hyphenated: non-singular matrix.

A nonsingular matrix is also called by some authors:

an invertible matrix

a regular matrix.

Also see

• Equivalence of Definitions of Nonsingular Matrix

• Results about nonsingular matrices can be found here.

Sources

• 2008: David Joyner: Adventures in Group Theory (2nd ed.) ... (previous) ... (next): Chapter $2$: 'And you do addition?': $\S 2.2$: Functions on vectors: $\S 2.2.5$: Determinants
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): non-singular