Determinants are scalar values computed from square matrices that encode important properties. The determinant measures whether a matrix is invertible ($\det \neq 0$), gives the volume scaling factor of the linear transformation, and appears in eigenvalue theory, Cramer rule, and change of variables.
Parents
Children
- Particular types of matrices
- Definition of trace of a matrix
- Cofactors
- Determinants and operations on matrices
- Determinants axiomatically
- The determinant of a matrix measures the area/volume of the parallelogram/parallelipiped determined by its columns.
- The determinant of the matrix of a linear transformation is the factor by which the area/volume changes.
- Definition of adjugate/classical adjoint of a matrix
- A matrix is called ill-conditioned if it is nearly singular
- The condition number of matrix measures how close it is to being singular