ABSTRACT

The strength of this textbook lies in the careful exposition of mathematical thinking, basic set-theoretic notions, and proof techniques combined with contemporary numerical methods used throughout the book. A basic version of computer programs compatible with the widely used program MatLab, and exercises are provided on a disk included with the book.Warmup * Matrix Operations * Invertible Matrices * Subspaces * Rank and Dimension * Geometry * Determinants-I * Diagonalization * Differential Equations * Hermitian Matrices * Triangular Matrices * Unitary Matrices * Block Diagonalization * Jordan Normal Form * Determinants-II * Proofs * Mathematical Induction†* Summary of MINIMAT * Answers * MINIMAT Tutorial (PC Version)

chapter 1|26 pages

WARMUP

chapter 2|46 pages

MATRIX OPERATIONS

chapter 3|42 pages

INVERTIBLE MATRICES

chapter 4|40 pages

SUBSPACES

chapter 5|34 pages

RANK AND DIMENSION

chapter 6|42 pages

GEOMETRY

chapter 7|22 pages

DETERMINANTS-I

chapter 8|24 pages

DIAGONALIZATION

chapter 9|28 pages

DIFFERENTIAL EQUATIONS

chapter 10|26 pages

HERMITIAN MATRICES

chapter 11|24 pages

TRIANGULAR MATRICES

chapter 12|24 pages

UNITARY MATRICES

chapter 13|22 pages

BLOCK DIAGONALIZATION

chapter 14|20 pages

JORDAN NORMAL FORM

chapter 15|16 pages

DETERMINANTS-II

chapter |8 pages

A: PROOFS

chapter |4 pages

B: MATHEMATIC ALINDUCTION

chapter C|16 pages

SUMMARY OF MINIMAT

chapter |58 pages

D: ANSWERS

chapter |14 pages

E: MINIMAT Tutorial (PC Version)