Linear Algebra/OLD/TOC

Old Pages
''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.''

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.


 * Linear Algebra/Laplace's Theorem
 * Linear Algebra/Cofactors and Minors
 * Linear Algebra/Fields
 * Linear Algebra/Systems of Linear Equations
 * 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 Spaces
 * Column and Row Spaces
 * Systems of Linear Equations
 * Row Reduction and Echelon Forms
 * The Matrix Equation Ax=b
 * Inner Product Spaces
 * Eigenvalues and Eigenvectors
 * Zero Matrices and Zero Vectors
 * Characteristic Equation
 * Cramer's Rule
 * Change of Basis
 * Introduction to Determinants
 * Partitioned Matrices
 * 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
 * Linear Transformations
 * Linear Transformations (should be looked through, and maybe rewritten as it is taken from the "old" book)
 * 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
 * The Inverse of a Matrix
 * Null spaces
 * Homogeneous Systems
 * Augmented Matrices ~