Basic Matrix Algebra With Algorithms And Applications / Edition 1

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Overview

Classroom tested with great success, this text builds the foundation in matrix algebra needed by freshman students in mathematics, physics, and computer science and by upper-level business and social science students. The author presents the material with outstanding pedagogical clarity, many figures and diagrams, and interrelated examples. The presentation relies heavily on the use of a graphing calculator, includes section summaries, and provides exercises in each chapter. Organized into bite-sized objectives, this relatively gentle treatment prepares readers well for the advanced studies their fields will require. Supporting material, including Maple worksheets, are available for download from the Internet. Integrates geometric and formal presentations that reinforce understanding and aid in retention Uses work with a graphing calculator overcome students' frustration and loss of focus that results from tedious arithmetic Incorporates recursive, nondeterministic algorithms to minimize abstraction and maximize clarity Offers a gentle introduction to proofs, recursion, and higher-dimensional geometry

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Product Details

  • ISBN-13: 9781584883333
  • Publisher: Taylor & Francis
  • Publication date: 12/1/2002
  • Series: Chapman Hall/CRC Mathematics Series
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 264
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.55 (d)

Table of Contents

SYSTEMS OF LINEAR EQUATIONS AND THEIR SOLUTION
Recognizing Linear Systems and Solutions
Matrices, Equivalence and Row Operations
Echelon Forms and Gaussian Elimination
Free Variables and General Solutions
The Vector Form of the General Solution
Geometric Vectors and Linear Functions
Polynomial Interpolation
MATRIX NUMBER SYSTEMS
Complex Numbers
Matrix Multiplication
Auxiliary Matrices and Matrix Inverses
Symmetric Projectors, Resolving Vectors
Least Squares Approximation
Changing Plane Coordinates
The Fast Fourier Transform and the Euclidean Algorithm.
DIAGONALIZABLE MATRICES
Eigenvectors and Eigenvalues
The Minimal Polynomial Algorithm
Linear Recurrence Relations
Properties of the Minimal Polynomial
The Sequence {Ak}
Discrete dynamical systems
Matrix compression with components
DETERMINANTS
Area and Composition of Linear Functions
Computing Determinants
Fundamental Properties of Determinants
Further Applications
Appendix: The abstract setting
Selected practice problem answers
Index

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