Invertible Matrix

linear-algebra

Definition

Invertible Matrix

A square matrix is called invertible if there exists a matrix such that:

The matrix is called the inverse of . Not invertible matrices are called singular matrices.

Properties

Let be two invertible matrices, then:

Invertibility

A square matrix is invertible if and only if its columns (or rows) are linearly independent. Thus, the columns (or rows) should form a basis of .

Determinant

Let and be the cofactors of a matrix .