An Introduction to Linear Algebra

To the Student Table of Contents Matrix Algebra Matrix Multiplication Systems of Linear Equations Criteria for Invertibility Exercises Vector Spaces Vector Space Axioms Subspaces Spans, Sums of Subspaces Bases and Dimension Exercises Euclidean Geometry Inner Products Orthogonal Projection The Determinant Exercises Linear Transformations Linear Transformations The Space of Linear Transformations The Rank-Nullity Theorem Exercises Diagonalization Linear Operators Eigenvalues and Eigenvectors The Characteristic Polynomial Symmetric Operators Applications Exercises Index