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All the Mathematics You Missed by Lori Pedersen, Thomas A. Garrity

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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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