A concise introduction to linear algebra for first-semester science students

Each section contains a problem set with solutions in the appendix

Focuses on precise definitions, uses helpful notations and illustrates results with numerous examples

Part I Systems of linear equations.- 1 Introduction.- 2 Systems with two equations and two unknowns.- 3 Gaussian elimination.- Part II Matrices and related topics.- 4 Basic operations.- 5 Linear dependence, bases, coordinates.- 6 Determinants.- Part III Complex numbers.- 7 Complex numbers: definition and operations.- 8 The Fundamental Theorem of Algebra.- 9 Linear systems with complex coefficients.- Part IV Vector spaces and linear maps.- 10 Vector spaces and their linear subspaces.- 11 Linear maps.- 12 Inner products on K-vector spaces.- Part V Eigenvalues and eigenvectors.- 13 Eigenvalues and eigenvectors of C-linear maps.- 14 Eigenvalues and eigenvectors of R-linear maps.- 15 Quadratic forms on Rn.- Part VI Differential equations.- 16 Introduction.- 17 Linear ODEs with constant coefficients of first order.- 18 Linear ODEs with constant coefficients of higher order.- Appendix A Solutions.