Singular and nonsingular matrices

  • 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.