Linear Algebra

__NOTOC__ Linear Algebra An Introduction to Mathematical Discourse notice float:right;margin-left:10px;margin-right:0px; padding:5px;font-size:120%;line-height:120%; left This book requires that you are familiar with calculus. This subject is covered by the wikibook Calculus. growth Printer.svg A printable version of Linear Algebra is available in two parts. Part 1[edit edit] contains everything from the beginning of the book through Chapter II. Part 2[edit edit] contains everything from Chapter III through the end of the book. This book discusses proof-based linear algebra. The book was designed specifically for students who have not previously been exposed to mathematics as mathematicians view it: that is, as a subject whose goal is to rigorously prove theorems starting from clear consistent definitions. This book attempts to build students up from a background where mathematics is simply a tool that provides useful calculations to the point where the students have a grasp of the clear and precise nature of mathematics. A more detailed discussion of the prerequisites and goal of this book is given in the introduction. Because of the proof-based nature of this book, readers are recommended to be familiar with mathematical proof before reading this book (although this is not a prerequisite, strictly speaking), so that their reading experiences can be smoother. To gain familiarity with mathematical proof and also some basic mathematical concepts, readers may read the wikibook Mathematical Proof. For a milder introduction to linear algebra that is not too proof-based, see the wikibook Introductory Linear Algebra. Table of Contents Cover Notation Introduction Linear Systems <li>Solving Linear Systems100% Jul 13, 2009 Gauss' Method 100% Jul 13, 2009 Describing the Solution Set 100% Jul 13, 2009 General = Particular + Homogeneous 100% Jul 13, 2009 Comparing Set Descriptions 100% Jul 13, 2009 Automation 100% Jul 13, 2009 <li>Linear Geometry of n-Space 100% Jul 13, 2009 Vectors in Space 100% Jul 13, 2009 Length and Angle Measures 100% Jul 13, 2009 <li>Reduced Echelon Form 100% Jul 13, 2009 Gauss-Jordan Reduction 100% Jul 13, 2009 Row Equivalence 100% Jul 13, 2009 <li>Topic: Computer Algebra Systems 100% Jul 13, 2009 <li>Topic: Input-Output Analysis 100% Jul 13, 2009 <li>Input-Output Analysis M File 100% Mar 24 2008 <li>Topic: Accuracy of Computations 100% Jul 13, 2009 <li>Topic: Analyzing Networks 100% Jul 13, 2009 <li>Topic: Speed of Gauss' Method 50% Mar 24, 2008 Vector Spaces 100% Apr 17, 2009 <li>Definition of Vector Space100% Apr 17, 2009 Definition and Examples100% Jun 18, 2009 Subspaces and Spanning sets100% Jun 18, 2009 <li>Linear Independence100% Apr 17, 2009 Definition and Examples100% Apr 17, 2009 <li>Basis and Dimension100% Apr 17, 2009 Basis100% Jun 18, 2009 Dimension100% Apr 17, 2009 Vector Spaces and Linear Systems100% Apr 17, 2009 Combining Subspaces100% Apr 17, 2009 <li>Topic: Fields100% Apr 17, 2009 <li>Topic: Crystals100% Apr 17, 2009 <li>Topic: Voting Paradoxes100% Apr 17, 2009 <li>Topic: Dimensional Analysis100% Apr 17, 2009 Maps Between Spaces <li>Isomorphisms100% Jun 21, 2009 Definition and Examples100% July 19, 2009 Dimension Characterizes Isomorphism100% Jun 21, 2009 <li>Homomorphisms100% Jun 21, 2009 Definition of Homomorphism100% Jun 21, 2009 Rangespace and Nullspace100% Jun 21, 2009 <li>Computing Linear Maps100% Jun 21, 2009 Representing Linear Maps with Matrices100% Jun 21, 2009 Any Matrix Represents a Linear Map100% Jun 21, 2009 <li>Matrix Operations100% Jun 21, 2009 Sums and Scalar Products100% Jun 21, 2009 Matrix Multiplication100% Jun 21, 2009 Mechanics of Matrix Multiplication100% Jun 21, 2009 Inverses100% Jun 21, 2009 <li>Change of Basis100% Jun 21, 2009 Changing Representations of Vectors100% Jun 21, 2009 Changing Map Representations100% Jun 21, 2009 <li>Projection100% Jun 21, 2009 Orthogonal Projection Onto a Line100% Jun 21, 2009 Gram-Schmidt Orthogonalization100% Jun 21, 2009 Projection Onto a Subspace100% Jun 21, 2009 <li>Topic: Line of Best Fit100% Jun 21, 2009 <li>Topic: Geometry of Linear Maps100% Jun 21, 2009 <li>Topic: Markov Chains100% Jun 21, 2009 <li>Topic: Orthonormal Matrices100% Jun 21, 2009 Determinants100% Jun 21, 2009 <li>Definition100% Jun 21, 2009 Exploration100% Jun 21, 2009 Properties of Determinants100% Jun 21, 2009 The Permutation Expansion100% Jun 21, 2009 Determinants Exist100% Jun 21, 2009 <li>Geometry of Determinants100% Jun 21, 2009 Determinants as Size Functions100% Jun 21, 2009 <li>Other Formulas for Determinants100% Jun 21, 2009 Laplace's Expansion100% Jun 21, 2009 <li>Topic: Cramer's Rule100% Jun 21, 2009 <li>Topic: Speed of Calculating Determinants100% Jun 21, 2009 <li>Topic: Projective Geometry100% Jun 21, 2009 Similarity100% Jun 24, 2009 <li>Complex Vector Spaces100% Jun 24, 2009 Factoring and Complex Numbers: A Review100% Jun 24, 2009 Complex Representations100% Jun 24, 2009 <li>Similarity Definition and Examples100% Jun 24, 2009 Diagonalizability100% Jun 24, 2009 Eigenvalues and Eigenvectors100% Jun 24, 2009 <li>Nilpotence100% Jun 24, 2009 Self-Composition100% Jun 24, 2009 Strings100% Jun 24, 2009 <li>Jordan Form100% Jun 24, 2009 Polynomials of Maps and Matrices100% Jun 24, 2009 Jordan Canonical Form100% Jun 24, 2009 <li>Topic: Geometry of Eigenvalues50% Jun 24, 2009 <li>Topic: The Method of Powers100% Jun 24, 2009 <li>Topic: Stable Populations100% Jun 24, 2009 <li>Topic: Linear Recurrences100% Jun 24, 2009 Unitary Transformations <li>Inner product spaces75% <li>Unitary and Hermitian matrices75% <li>Singular Value Decomposition75% <li>Spectral Theorem75% Appendix The following is a brief overview of some basic concepts in mathematics. For more details, reader can read the wikibook Mathematical Proof. Propositions Quantifiers Techniques of Proof Sets, Functions, Relations Resources and Licensing Licensing And History Resources Bibliography (see individual pages for references) Index100% Apr 22, 2010 Algebra University level mathematics books L 100% Category:Books with print version