Chapter 1

Linear Algebra

Basic Object: | Vector Spaces |

Basic Map: | Linear Transformations |

Basic Goal: | Equivalences for the Invertibility of Matrices |

1.1 Introduction

Though a bit of an exaggeration, it can be said that a mathematical problem can be solved only if it can be reduced to a calculation in linear algebra. And a calculation in linear algebra will reduce ultimately to the solving of a system of linear equations, which in turn comes down to the manipulation of matrices. Throughout this text and, more importantly, throughout mathematics, ...

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