Linear Algebra A Geometric Approach

by Shifrin, Ted; Adams, Malcolm

• ISBN13: 9780716743378
• ISBN10: 071674337X
• Edition: 1st
• Format: Hardcover
• Copyright: 2001-08-24
• Publisher: W. H. Freeman

Summary

Introducing students to a subject that lies at the foundations of modern mathematics, physics, statistics, and many other disciplines,Linear Algebra: A Geometric Approachappeals to science and engineering students as well as mathematics students making the transition to more abstract advanced courses. One of the goals of this text is to help students learn to think about mathematical concepts and to write rigorous mathematical arguments. The authors do not presuppose any exposure to vectors or vector algebra, and only a passing acquaintance with the derivative and integral is required for certain (optional) topics.

Table of Contents

Preface	vii
Foreword to the Instructor	xiii
Foreword to the Student	xvii
Vectors and Matrices	1	(94)
Vectors	2	(19)
Dot Product	21	(12)
Hyperplanes in Rn	33	(10)
Systems of Linear Equations and Gaussian Elimination	43	(19)
The Theory of Linear Systems	62	(14)
Some Applications	76	(19)
Matrix Algebra	95	(43)
Matrix Operations	95	(23)
Inverse Matrices	118	(13)
The Transpose	131	(7)
Vector Spaces	138	(79)
Subspaces of Rn	138	(18)
Linear Independence	156	(11)
Basis and Dimension	167	(10)
The Four Fundamental Subspaces	177	(14)
A Graphic Example	191	(7)
Abstract Vector Spaces	198	(19)
Projections and Linear Transformations	217	(56)
Inconsistent Systems and Projection	217	(12)
Orthogonal Bases	229	(11)
Linear Transformations	240	(16)
Change of Basis	256	(17)
Determinants	273	(30)
Signed Area in R2	273	(6)
Determinants	279	(11)
Cofactors and Cramer's Rule	290	(13)
Eigenvalues and Eigenvectors	303	(48)
The Characteristic Polynomial	304	(11)
Diagonalizability	315	(8)
Applications	323	(12)
The Spectral Theorem	335	(16)
Further Topics	351	(66)
Complex Eigenvalues and Jordan Canonical Form	351	(19)
Computer Graphics and Geometry	370	(23)
Matrix Exponentials and Differential Equations	393	(24)
For Further Reading	417	(2)
Answers to Selected Exercises	419	(16)
Index	435