- A matrix is singular if it cannot be inverted, and nonsingular if it can be inverted.
- A matrix is singular if its determinant is zero.
- A matrix is nonsingular if its determinant is not zero.
- A matrix that is singular cannot be used to find unique solutions to a system of linear equations.
- Nonsingular matrices are important in mathematics and are used in a variety of applications, such as solving systems of equations and transforming data.
Formulas:
- A matrix A is singular if and only if |A| = 0.
- A matrix A is nonsingular (or invertible) if and only if |A| is nonzero.