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LinAlg_VectorSpaces

# LinAlg_VectorSpaces - LINEARALGEBRA VectorSpaces...

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LINEAR ALGEBRA Vector Spaces Paul Dawkins

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Linear Algebra © 2007 Paul Dawkins i http://tutorial.math.lamar.edu/terms.aspx Table of Contents Preface ............................................................................................................................................ ii Vector Spaces ................................................................................................................................. 3 Introduction ................................................................................................................................................ 3 Vector Spaces ............................................................................................................................................. 5 Subspaces ................................................................................................................................................. 15 Span .......................................................................................................................................................... 25 Linear Independence ................................................................................................................................ 34 Basis and Dimension ................................................................................................................................ 45 Change of Basis ....................................................................................................................................... 61 Fundamental Subspaces ........................................................................................................................... 74 Inner Product Spaces ................................................................................................................................ 85 Orthonormal Basis ................................................................................................................................... 93 Least Squares .......................................................................................................................................... 105 QR-Decomposition ................................................................................................................................. 113 Orthogonal Matrices ............................................................................................................................... 121