Applied Mathematical Methods

2

Matrices and Linear Transformations

In this chapter, we shall discuss the basic conceptual notions of matrices and linear transformations, and examine the underlying correspondence between algebra and geometry. By convention,

1. a vector is typically treated as a column vector, as in
   

   sometimes necessitating representations like a^T to denote a row vector in theoretical formulations, where a itself is a column vector, and

2. we typically denote vectors and matrices with boldface letters, often small letters for vectors and capital ones for matrices.

The reader is supposed to be aware of the basic operations of matrices and determinants. As such, ...