# 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

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