Multidimensional Signal and Color Image Processing Using Lattices

Appendix CVector Spaces

This appendix briefly summarizes some of the key results from linear algebra that are used in this book. A great more detail can be found in standard texts, such as Hoffman and Kunze (1971), Shaw (1982), and Olver and Shakiban (2006).

1. 1. A general vector space is defined with respect to a field . In this book, we will only be concerned with real and complex vector spaces defined with respect to the fields and of real and complex numbers. The development is carried out for complex vector spaces, since it is then easy to restrict everything to be real. In this appendix, elements of a vector space are denoted in boldface with an arrow over them, e.g., . Several different types of vector spaces appear in the main text, and they don't generally use this notation.
2. 2. A complex vector space is a set on which two operations are defined,

   vector addition ,

   multiplication ...