Elementary Linear Algebra - K. R. MATTHEWS

# Elementary Linear Algebra - K. R. MATTHEWS - ELEMENTARY...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ELEMENTARY LINEAR ALGEBRA K. R. MATTHEWS DEPARTMENT OF MATHEMATICS UNIVERSITY OF QUEENSLAND Second Online Version, December 1998 Comments to the author at [email protected] All contents copyright c 1991 Keith R. Matthews Department of Mathematics University of Queensland All rights reserved Contents 1 LINEAR EQUATIONS 1 1.1 Introduction to linear equations . . . . . . . . . . . . . . . . . 1 1.2 Solving linear equations . . . . . . . . . . . . . . . . . . . . . 6 1.3 The Gauss–Jordan algorithm . . . . . . . . . . . . . . . . . . 8 1.4 Systematic solution of linear systems. . . . . . . . . . . . . . 9 1.5 Homogeneous systems . . . . . . . . . . . . . . . . . . . . . . 16 1.6 PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2 MATRICES 23 2.1 Matrix arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.2 Linear transformations . . . . . . . . . . . . . . . . . . . . . . 27 2.3 Recurrence relations . . . . . . . . . . . . . . . . . . . . . . . 31 2.4 PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.5 Non–singular matrices . . . . . . . . . . . . . . . . . . . . . . 36 2.6 Least squares solution of equations . . . . . . . . . . . . . . . 47 2.7 PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3 SUBSPACES 55 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.2 Subspaces of F n . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.3 Linear dependence . . . . . . . . . . . . . . . . . . . . . . . . 58 3.4 Basis of a subspace . . . . . . . . . . . . . . . . . . . . . . . . 61 3.5 Rank and nullity of a matrix . . . . . . . . . . . . . . . . . . 64 3.6 PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4 DETERMINANTS 71 4.1 PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 i 5 COMPLEX NUMBERS 89 5.1 Constructing the complex numbers . . . . . . . . . . . . . . . 89 5.2 Calculating with complex numbers . . . . . . . . . . . . . . . 91 5.3 Geometric representation of C . . . . . . . . . . . . . . . . . . 95 5.4 Complex conjugate . . . . . . . . . . . . . . . . . . . . . . . . 96 5.5 Modulus of a complex number . . . . . . . . . . . . . . . . . 99 5.6 Argument of a complex number . . . . . . . . . . . . . . . . . 103 5.7 De Moivre’s theorem . . . . . . . . . . . . . . . . . . . . . . . 107 5.8 PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 6 EIGENVALUES AND EIGENVECTORS 115 6.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 6.2 Definitions and examples . . . . . . . . . . . . . . . . . . . . . 118 6.3 PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 7 Identifying second degree equations 129 7.1 The eigenvalue method . . . . . . . . . . . . . . . . . . . . . . 129 7.2 A classification algorithm . . . . . . . . . . . . . . . . . . . . 141 7.3 PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 8 THREE–DIMENSIONAL GEOMETRY 149 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1498....
View Full Document

{[ snackBarMessage ]}

### Page1 / 301

Elementary Linear Algebra - K. R. MATTHEWS - ELEMENTARY...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online