### Abstract

‘Determinants and matrices’ explains that in three dimensions, the absolute value of the determinant *det(A)* of a linear transformation represented by the matrix *A* is the multiplier of volume. The columns of *A* are the images of the position vectors of the sides of the unit cube and they define a three-dimensional version of a parallelogram, a parallelepiped, the volume of which is *|det(A)|*. It goes on to describe the properties and applications of determinants to networks (using the Kirchhoff matrix); Cramer’s Rule; eigenvalues; and eigenvectors, which are fundamental in linear mathematics. Other key topics in matrix theory—similarity, diagonalization, and factorization of matrices—are also discussed.