Chapter 2 Matrices and Determinants

In this chapter, we review some of the basic results from the theory of matrices and determinants.

2.1 Matrices

Let us denote by Mat m × n the set of m × n matrices (that is, m rows and n columns) with real entries. When m = n , we say that the matrices are square. It is easily shown that with the usual matrix addition and scalar multiplication, Mat m × n is a vector space, and that with the usual matrix multiplication, Mat m × m is a ring.

Let P be a matrix in Mat m × n , with


The transpose of P is the matrix P T in Mat n × m defined by


The row matrices of P are


and the column matrices of P are


Get Semi-Riemannian Geometry now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.