ABSTRACT
This chapter addresses the concept of linear vector spaces and normed and inner product spaces with applications in signal and image processing, communication and color engineering. It discusses orthogonal vectors in a given vector space with applications such as Fourier series and discrete Fourier transform. Linear vector space is an important concept in linear algebra. Linear vector spaces have applications in different fields of engineering. In the discipline of electrical engineering, vector spaces are extensively used in detection and estimation theory, color engineering, signal and image processing and statistical communication theory. The minimal spanning set of a vector space forms the basis vector set for that space. Schwarz’s inequality is an extremely useful inequality used in different engineering optimization problems. As an example, it is used to derive the matched filter as well as the maximum ratio combining technique found in digital communication systems. A complete inner product space is called a Hilbert space.
