Determinants

Determinant is a scalar associated with a square matrix in a particular way. One of the most important uses of determinants within Linear Algebra is in the study of eigenvalues (Chapter 8). They also occur in Cramer’s rule for solving linear equations and can be used to give a formula for the inverse of a non-singular matrix. In the Calculus of several variables, the Jacobian used in transforming a multiple integral uses determinant. This use arises from the fact that determinant is the volume of a certain parallelopiped. Determinants are also useful in various other subjects like Physics, Astronomy and Statistics.