Book:Richard Kaye/Linear Algebra

Subject Matter

 * Linear Algebra

Contents

 * Preface


 * PART I MATRICES AND VECTOR SPACES


 * 1 Matrices


 * 2 Vector spaces


 * PART II BILINEAR AND SESQUILINEAR FORMS


 * 3 Inner product spaces


 * 4 Bilinear and sesquilinear forms


 * 5 Orthogonal bases


 * 6 When is a form definite?


 * 7 Quadratic forms and Sylvester's law of inertia


 * PART III LINEAR TRANSFORMATIONS


 * 8 Linear transformations


 * 9 Polynomials


 * 10 Eigenvalues and eigenvectors


 * 11 The minimum polynomial


 * 12 Diagonalization


 * 13 Self-adjoint transformations


 * 14 The Jordan normal form


 * Appendix A A Theorem of Analysis


 * Appendix B Applications to quantum mechanics


 * Index