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Classification, Parameter Estimation and State Estimation: An Engineering Approach Using MATLAB by David M. J. Tax, Dick de Ridder, Ferdinand van der Heijden, Robert Duin

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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. images and images. 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 images and images 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:

images

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 hn,m (the elements) on an orthogonal grid of N rows and M columns:

images

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

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