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