Whereas Appendix A deals with general linear spaces and linear operators, the current appendix restricts attention to linear spaces with finite dimension, that is ℝ* ^{N}* and ℂ

Vectors in ℝ* ^{N}* and ℂ

(B.1)

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}*

(B.2)

The elements are real or complex. Vectors can be regarded as *N* × 1 matrices (column vectors) or 1 × *M* matrices (row vectors). A matrix can be regarded as a horizontal arrangement of *M* column vectors with dimension *N*, for example:

(B.3)

Of course, a matrix can also be regarded as a vertical arrangement of *N* row vectors.

The *scalar–matrix multiplication α***H**

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