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

equation

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

equation

The row matrices of P are

equation

and the column matrices of P are

equation

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