Adaptive Filtering

1

Vectors

1.1    INTRODUCTION

In this text we present vectors with boldfaced lowercase Latin letters, in columnar format. Matrices are presented with boldfaced capital Latin letters and numbers with lowercase Latin letters. For example, for three different types of three element vectors, we write

$\mathit{x}=\left[\begin{array}{l}1\\ 2.3\\ -2\end{array}\right];\mathit{y}=\left[\begin{array}{l}{y}_1\\ y_2\\ y_3\end{array}\right];\mathit{z}=\left[\begin{array}{l}2.33\\ 4+j5\\ -j\end{array}\right]$

(1.1)

The elements y₁, y₂, and y₃ are constants. For any one of the above vectors, we could also write its equivalent form, for example, $x^T=\left[\begin{array}{ccc}1& 2.3& -2\end{array}\right]$ or x^T=(1, 2.3, −2), where the letter T stands for the word transpose. The MATLAB^® column vector format is written in the command window as follows:

>>x = [1 2.3 −2]’;%column vector, accent indicates transpose;

>>x = [1; 2.3; −2];%column ...