Invertible

A n x n matrix A is invertible if there exists a matrix A^-1 such that AA^-1 = A^-1A = I. This is only a conceivable operation when A is a square matrix.

A^-1 exists only when the dimension of the column space of A, or the rank of the A, is equal to n. That is, it only exists when the columns of A form a basis for Rⁿ.

The algorithm described in How to find the inverse of a matrix will always find the inverse if it exists.

In*vert"i*ble (?), a. [From Invert.]

1.

Capable of being inverted or turned.

2. Chem.

Capable of being changed or converted; as, invertible sugar.

© Webster 1913.

In*vert"i*ble, a. [Pref. in- not + L. vertere to turn + -ible.]

Incapable of being turned or changed.

An indurate and invertible conscience. Cranmer.

© Webster 1913.