2.1 A Very Brief Overview of Matrix Linear Algebra

This section defines notational conventions and matrix operations used throughout the text and provides a brief summary of some matrix linear algebra concepts within the context of MATLAB®. An extremely good reference for the matrix operations and formulas presented in this section can be found online in Ref. [1].

2.1.1 Vector and Matrix Conventions and Notation

A scalar will usually be presented as lower case, a, a vector as lower case bold, a, and a matrix as upper case bold, A.

An n-vector is the n × 1 column vector

(2.1) equation

By convention, all vectors will be column vectors. It follows immediately that one can write a column vector as the transpose of a row vector (especially useful to conserve space in a report or journal article)

(2.2) equation

with commas separating the elements of the vector. img represent a vector or matrix transpose, which will be defined below.

An n × m matrix is a two-dimensional array of the form

(2.3) equation

The first dimension is the number of rows and the second is the number of columns. The ij th component of the matrix ...

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