# Appendix B

# Topics Selected from Linear Algebra and Matrix Theory

Whereas Appendix A deals with general linear spaces and linear operators, the current appendix restricts the attention to linear spaces with finite dimension, i.e. and . With that, all that has been said in Appendix A also holds true for the topics of this appendix.

## B.1 VECTORS AND MATRICES

Vectors in and are denoted by bold-faced letters, e.g. **f, g**. The elements in a vector are arranged either vertically (a column vector) or horizontally (a row vector). For example:

The superscript ^{T} is used to convert column vectors to row vectors. Vector addition and scalar multiplication are defined as in Section A.1.

A *matrix* **H** with dimension *N* × *M* is an arrangement of *NM* numbers *h*_{n,m} (the elements) on an orthogonal grid of *N* rows and *M* columns:

The elements are real or complex. Vectors can be regarded as *N* × 1 matrices (column ...