Chapter 11

# Matrix Calculus and Euclidean Vector Space

This book uses several elements of algebra, specifically matrix calculus and the notion of spaces endowed with a distance (or a metric). To help users avoid having to read a general algebra book, we have grouped these elements together. These examples do not need to be read in any particular order, given that each one uses elements of the other.

## 11.1 Matrix Calculus

#### Definitions

A matrix is a set of numbers organised in a rectangular table. It is generally denoted by a capital letter (for example, X). Its terms (= elements = entries) are designated using indices, the first being that of the rows (for example, A12, at the crossing of the first row and the second column).

The dimensions of a ...

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