Determinant: meaning, definitions and examples

mathematics

In mathematics, a determinant is a scalar value that can be computed from the elements of a square matrix. It encapsulates key information about the matrix, including whether the matrix is invertible and the volume scaling factor of the linear transformation described by the matrix. The determinant is denoted as det(A) for a matrix A and can be calculated using various methods, including cofactor expansion or row reduction. Determinants are particularly significant in solving systems of linear equations and in linear algebra applications.

determinative, factor

Examples of usage

• To determine if the matrix is invertible, calculate its determinant.

• The area of the parallelogram can be found using the determinant of vectors.

• The determinant of the identity matrix is always one.