PrefaceNotations and ConventionsChapter 1 Euclidean Spaces1.1 Vectors1.2 Lines in R2 1.3 Length and Dot Product1.4 Orthogonal Projection1.5 Area in R2 and 2×2 Determinants1.6 Planes in R3Chapter 2 System of Linear Equations2.1 Terminologies and Definitions2.2 Gaussian EliminationChapter 3 Matrix Algebra3.1 Definitions and Properties of Matrix Operations3.2 Linear Systems Revisited 3.3 Invertible Matrix3.4 Square Matrices of Special Forms3.5 Elementary MatricesChapter 4 Determinants4.1 Definition4.2 Properties of Determinants4.3 Adjoint Matrix and Cramer's Rule4.4 Cross Product in R3Chapter 5 Subspaces of Rn and Their Bases5.1 Subspaces of Rn5.2 Linear Combination and Linear Independence5.3 Basis and Dimension5.4 Coordinates with Respect to Ordered BasesChapter 6 Linear Transformations6.1 Matrix Transformations6.2 Linear Operators on R2 and R3Chapter 7 Eigenvalues, Eigenvectors and Diagonalization7.1 Definitions and Properties of Eigenvalues and Eigenvectors7.2 Diagonalizability7.3 DiagonalizationAnswer Keys to Selected Exercise ProblemsSuggested Further ReadingsIndex