9780471669609

Elementary Linear Algebra, 9th Edition

by
  • ISBN13:

    9780471669609

  • ISBN10:

    0471669601

  • Edition: 9
  • Format: Hardcover
  • Copyright: 12/1/2004
  • Publisher: WILEY
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Summary

This classic treatment of linear algebra presents the fundamentals in the clearest possible way, examining basic ideas by means of computational examples and geometrical interpretation. It proceeds from familiar concepts to the unfamiliar, from the concrete to the abstract. Readers consistently praise this outstanding text for its expository style and clarity of presentation. Clear, accessible, step-by-step explanations make the material crystal clear. The authors spotlight the relationships between concepts to give a unified and complete picture. Established the intricate thread of relationships between systems of equations, matrices, determinants, vectors, linear transformations and eigenvalues.

Table of Contents

Systems of Linear Equations and Matrices
1(82)
Introduction to Systems of Linear Equations
2(6)
Gaussian Elimination
8(15)
Matrices and Matrix Operations
23(16)
Inverses; Rules of Matrix Arithmetic
39(12)
Elementary Matrices and a Method for Finding A-1
51(9)
Further Results on Systems of Equations and Invertibility
60(8)
Diagonal, Triangular, and Symmetric Matrices
68(15)
Determinants
83(40)
Determinants by Cofactor Expansion
84(12)
Evaluating Determinants by Row Reduction
96(7)
Properties of the Determinant Function
103(8)
A Combinatorial Approach to Determinants
111(12)
Vectors in 2-Space and 3-Space
123(44)
Introduction to Vectors (Geometric)
124(7)
Norm of a Vector; Vector Arithmetic
131(5)
Dot Product; Projections
136(8)
Cross Product
144(12)
Lines and Planes in 3-Space
156(11)
Euclidean Vector Spaces
167(54)
Euclidean n-Space
168(13)
Linear Transformations from Rn to Rm
181(16)
Properties of Linear Transformations from Rn to Rm
197(13)
Linear Transformations and Polynomials
210(11)
General Vector Spaces
221(74)
Real Vector Spaces
222(7)
Subspaces
229(11)
Linear Independence
240(10)
Basis and Dimension
250(16)
Row Space, Column Space, and Nullspace
266(13)
Rank and Nullity
279(16)
Inner Product Spaces
295(64)
Inner Products
296(11)
Angle and Orthogonality in Inner Product Spaces
307(11)
Orthonormal Bases; Gram--Schmidt Prodcess; Q R-Decomposition
318(14)
Best Approximation; Least Squares
332(9)
Change of Basis
341(6)
Orthogonal Matrices
347(12)
Eigenvalues, Eigenvectors
359(30)
Eigenvalues and Eigenvectors
360(9)
Diagonalization
369(11)
Orthogonal Diagonalization
380(9)
Linear Transformations
389(62)
General Linear Transformations
390(10)
Kernel and Range
400(7)
Inverse Linear Transformations
407(9)
Matrices of General Linear Transformations
416(14)
Similarity
430(12)
Isomorphism
442(9)
Additional Topics
451(70)
Application to Differential Equations
452(6)
Geometry of Linear Operators on R2
458(10)
Least Squares Fitting to Data
468(6)
Approximation Problems; Fourier Series
474(5)
Quadratic Forms
479(8)
Diagonalizing Quadratic Forms; Conic Sections
487(10)
Quadric Surfaces
497(5)
Comparison of Procedures for Solving Linear Systems
502(9)
LU-Decompositions
511(10)
Complex Vector Spaces
521(46)
Complex Numbers
522(6)
Division of Complex Numbers
528(5)
Polar Form of a Complex Number
533(7)
Complex Vector Spaces
540(7)
Complex Inner Product Spaces
547(7)
Unitary Normal, and Hermitian Matrices
554(13)
Answers to Exercises 567(32)
Index 599

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