9. Determinants and matrices
- Peter M. Higgins
‘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.