Linear Algebra/OLD/TOC

Old Pages This "book" consists of 2 parts: Fragmented pages from the old book, and a recently donated book. This book needs to be cleaned up. This remaining material on this page was the start of a much less complete linear algebra book. Much of the material here may be useful and could potentially be merged into the main book. Algebra Advanced Linear algebra is a branch of algebra in mathematics concerned with the study of vectors, vector spaces, linear transformations, and systems of linear equations. Vector spaces are very important in modern mathematics. Linear algebra is widely used in abstract algebra and functional analysis. It has extensive applications in natural and social sciences, for both linear systems and linear models of nonlinear systems. It is part of the study of Abstract Algebra. General Information and MoS This book is meant for students who wish to study linear algebra from scratch. The approach will not be entirely informal. Every result in the book is intended to be either proved or justified by some mathematical procedure. Links to tedious proofs can be made to Famous Theorems of Mathematics/Algebra after the proof is written there. Exercises Learning to think is extremely important in mathematics. Therefore in this book exercises form an important component and by no means should be ignored. Many important concepts of linear algebra are developed via the exercises in the book. It is necessary that before proceeding to the next chapter, the student does the exercises. Links to hints and solutions to many of the exercises are provided but they should be only used in cases of difficulty. These sections are left over remnants from other book projects, and need to be incorporated into the pages above. Linear Algebra/Laplace's Theorem Linear Algebra/Cofactors and Minors Linear Algebra/Fields Linear Algebra/Systems of Linear Equations 100% Mar 12, 2008 Invariant Subspaces Matrices General Systems General Solutions Vector Spaces Linear Dependence Bases and dimensions Subspaces Direct Sum Quotient Space Span of a set Hyperplanes Linear Dependence Matrices and Determinants Cofactors and Minors Cramer's Rule Null Spaces100% May 25, 2007 Column and Row Spaces100% May 25, 2007 Systems of Linear Equations 50% Oct 9, 2006 Row Reduction and Echelon Forms 50% Apr 13, 2007 The Matrix Equation Ax=b Inner Product Spaces 25% May 11, 2007 Eigenvalues and Eigenvectors Zero Matrices and Zero Vectors 25% Apr 13, 2007 Characteristic Equation Cramer's Rule 75% Oct 20, 2006 Change of Basis50% Jun 27, 2007 Introduction to Determinants 25% May 11, 2007 Partitioned Matrices 25% Apr 13, 2007 Vector Spaces And Subspaces (Need attention as this is a page from the old book) Inner Product, Length, and Orthogonality (It is a stub) Orthogonal Sets Basis Vectors 25% Oct 20, 2006 Linear Transformations 25% May 11, 2007 Linear Transformations (should be looked through, and maybe rewritten as it is taken from the "old" book) 25% Oct 20, 2006 Linear Algebra/Linear transformations Glossary Linear Algebra/Vectors Linear Algebra/Eigenvalues and eigenvectors Linear Algebra/Row and Column Operations Linear Algebra/OLD/Vector Spaces Linear Algebra/OLD/Matrix Operations Linear Algebra/OLD/Eigenvalues and Eigenvectors Linear Algebra/OLD/Change of Basis Linear Algebra/Matrix Inverses Linear Algebra/Determinant Linear Algebra/Inner product spaces Row and column spaces Potential use in "Linear Algebra for Scientists and Engineers" Matrices and Vectors Matrix Operations 50% Jun 27, 2007 The Inverse of a Matrix 25% May 11, 2007 Null spaces Homogeneous Systems Augmented Matrices 75% Oct 17, 2006~