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Linear Algebra: Ideas and Applications 5th edition [Hardback]

(Purdue University)
  • Formāts: Hardback, 512 pages, height x width x depth: 231x158x28 mm, weight: 907 g
  • Izdošanas datums: 19-Mar-2021
  • Izdevniecība: John Wiley & Sons Inc
  • ISBN-10: 1119656923
  • ISBN-13: 9781119656920
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  • Hardback
  • Cena: 133,98 €
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  • Formāts: Hardback, 512 pages, height x width x depth: 231x158x28 mm, weight: 907 g
  • Izdošanas datums: 19-Mar-2021
  • Izdevniecība: John Wiley & Sons Inc
  • ISBN-10: 1119656923
  • ISBN-13: 9781119656920
Citas grāmatas par šo tēmu:
"This book teaches the computational, application, and deeper, more abstract aspects of linear algebra in parallel. The author incorporates computational projects in every topic. This book is written with constant attention to student readability using input from experts in pedagogy. Features of this book include: gradual development of vector spaces, treatment of linear dependence and independence, numerous theoretical, but concrete exercises, many applications sections for self-study or classroom use, and numerous computer projects/exercises using MATLAB. This new edition contains many new and expanded exercises, new computer labs, a more detailed Table of Contents, and discussion of the four fundamental subspaces of a matrix. This book is suitable fora one or a two-semester class"--

Praise for the Third Edition

"This volume is ground-breaking in terms of mathematical texts in that it does not teach from a detached perspective, but instead, looks to show students that competent mathematicians bring an intuitive understanding to the subject rather than just a master of  applications."

                  - Electric Review

Learn foundational and advanced topics in linear algebra with this concise and approachable resource

A comprehensive introduction, Linear Algebra: Ideas and Applications, Fifth Edition provides a discussion of the theory and applications of linear algebra that blends abstract and computational concepts. With a focus on the development of mathematical intuition, the book emphasizes the need to understand both the applications of a particular technique and the mathematical ideas underlying the technique. 

The book introduces each new concept in the context of explicit numerical examples, which allows the abstract concepts to grow organically out of the necessity to solve specific problems. The intuitive discussions are consistently followed by rigorous statements of results and proofs. Linear Algebra: Ideas and Applications, Fifth Edition also features:

  • A new application section on section on Google’s Page Rank Algorithm.
  • A new application section on pricing long term health insurance at a Continuing Care Retirement Community (CCRC).
  • Many other illuminating applications of linear algebra with self-study questions for additional study.
  • End-of-chapter summaries and sections with true-false questions to aid readers with further comprehension of the presented material
  • Numerous computer exercises throughout using MATLAB® code

Linear Algebra: Ideas and Applications, Fifth Edition is an excellent undergraduate-level textbook for one or two semester undergraduate courses in mathematics, science, computer science, and engineering.  With an emphasis on intuition development, the book is also an ideal self-study reference.

Preface xi
Features Of The Text xiii
Acknowledgments xvii
About The Companion Website xviii
1 Systems Of Linear Equations
1(92)
1.1 The Vector Space of m × n Matrices
1(26)
The Space Rn
4(3)
Linear Combinations and Linear Dependence
7(4)
What Is a Vector Space?
11(4)
Why Prove Anything?
15(1)
Exercises
16(6)
1.1.1 Computer Projects/Exercises/Exercises
22(2)
Exercises
24(1)
1.1.2 Applications to Graph Theory I
25(2)
Exercises
27(1)
1.2 Systems
27(19)
Rank: The Maximum Number of Linearly Independent Equations
34(3)
Exercises
37(2)
1.2.1 Computer Projects/Exercises
39(1)
Exercises
39(1)
1.2.2 Applications to Circuit Theory
40(4)
Exercises
44(2)
1.3 Gaussian Elimination
46(25)
Spanning in Polynomial Spaces
56(3)
Computational Issues: Pivoting
59(1)
Exercises
60(6)
1.3.1 Using tolerances in MATLAB's rref and rank
66(1)
Using Tolerances in rref and Rank
66(1)
Exercises
67(1)
1.3.2 Applications to Traffic Flow
68(2)
Exercises
70(1)
1.4 Column Space and Nullspace
71(22)
Subspaces
74(8)
Exercises
82(7)
1.4.1 Computer Projects/Exercises
89(1)
Exercises
90(1)
Chapter Summary
91(2)
2 Linear Independence And Dimension
93(54)
2.1 The Test for Linear Independence
93(16)
Bases for the Column Space
100(2)
Testing Functions for Independence
102(2)
Exercises
104(4)
2.1.1 Computer Projects/Exercises
108(1)
Exercises
108(1)
2.2 Dimension
109(19)
Exercises
118(5)
2.2.1 Computer Projects/Exercises
123(1)
Exercises
123(2)
2.2.2 Applications to Differential Equations
125(3)
Exercises
128(1)
2.3 Row Space and the Rank-Nullity Theorem
128(19)
Bases for the Row Space
130(8)
Computational Issues: Computing Rank
138(2)
Exercises
140(3)
2.3.1 Computer Projects/Exercises
143(1)
Exercises
143(1)
Chapter Summary
144(3)
3 Linear Transformations
147(98)
3.1 The Linearity Properties
147(15)
Exercises
155(5)
3.1.1 Computer Projects/Exercises
160(1)
Exercises
161(1)
3.2 Matrix Multiplication (Composition)
162(22)
Partitioned Matrices
169(2)
Computational Issues: Parallel Computing
171(1)
Exercises
171(6)
3.2.1 Computer Projects/Exercises
177(1)
3-D Computer Graphics
177(1)
Exercises
177(1)
3.2.2 Applications to Graph Theory II
178(2)
Exercises
180(1)
3.2.3 Computer Projects/Exercises
180(1)
Google's Page Rank Algorithm
180(3)
Exercises
183(1)
3.3 Inverses
184(21)
Computational Issues: Reduction versus Inverses
190(2)
Exercises
192(5)
3.3.1 Computer Projects/Exercises
197(1)
Ill-Conditioned Systems
197(1)
Exercises
197(2)
3.3.2 Applications to Economics: The Leontief Open Model
199(5)
Exercises
204(1)
3.4 The LU Factorization
205(12)
Exercises
213(3)
3.4.1 Computer Projects/Exercises
216(1)
Exercises
216(1)
3.5 The Matrix of a Linear Transformation
217(28)
Coordinates
217(8)
Application to Differential Equations
225(3)
Isomorphism
228(1)
Invertible Linear Transformations
229(2)
Exercises
231(5)
3.5.1 Computer Projects/Exercises
236(1)
Graphing in Skewed-Coordinates
236(1)
Exercises
236(1)
3.5.2 Computer Projects/Exercises
237(1)
Pricing Long Term Health Care Insurance
237(5)
Exercises
242(1)
Chapter Summary
242(3)
4 Determinants
245(34)
4.1 Definition of the Determinant
245(14)
4.1.1 The Rest of the Proofs
252(4)
Exercises
256(2)
4.1.2 Computer Projects/Exercises
258(1)
4.2 Reduction and Determinants
259(12)
Exercises
266(2)
4.2.1 Volume
268(3)
Exercises
271(1)
4.3 A Formula for Inverses
271(8)
Exercises
275(1)
Chapter Summary
276(3)
5 Eigenvectors And Eigenvalues
279(38)
5.1 Eigenvectors
279(16)
Exercises
288(3)
5.1.1 Computer Projects/Exercises
291(1)
Exercises
291(1)
5.1.2 Application to Markov Chains
291(3)
Exercises
294(1)
5.2 Diagonalization
295(9)
Powers of Matrices
297(2)
Exercises
299(2)
5.2.1 Application to Systems of Differential Equations
301(3)
Exercises
304(1)
5.3 Complex Eigenvectors
304(13)
Complex Vector Spaces
311(1)
Exercises
312(2)
5.3.1 Computer Projects/Exercises
314(1)
Exercises
314(1)
Chapter Summary
314(3)
6 Orthogonality
317(104)
6.1 The Scalar Product in Rn
317(11)
Orthogonal/Orthonormal Bases and Coordinates
321(5)
Exercises
326(2)
6.2 Projections: The Gram-Schmidt Process
328(14)
The QR Decomposition
334(3)
Uniqueness of the QR Factorization
337(1)
Exercises
338(3)
6.2.1 Computer Projects/Exercises
341(1)
Exercises
342(1)
6.3 Fourier Series: Scalar Product Spaces
342(13)
Exercises
350(3)
6.3.1 Computer Projects/Exercises
353(1)
Exercises
354(1)
6.4 Orthogonal Matrices
355(15)
Householder Matrices
360(4)
Exercises
364(5)
6.4.1 Computer Projects/Exercises
369(1)
Exercises
369(1)
6.5 Least Squares
370(11)
Exercises
377(3)
6.5.1 Computer Projects/Exercises
380(1)
Exercises
380(1)
6.6 Quadratic Forms: Orthogonal Diagonalization
381(15)
The Spectral Theorem
384(1)
The Principal Axis Theorem
385(7)
Exercises
392(2)
6.6.1 Computer Projects/Exercises
394(1)
Exercises
395(1)
6.7 The Singular Value Decomposition (SVD)
396(13)
Application of the SVD to Least-Squares Problems
402(2)
Exercises
404(2)
Computing the SVD Using Householder Matrices
406(2)
Diagonalizing Matrices Using Householder Matrices
408(1)
6.8 Hermitian Symmetric and Unitary Matrices
409(12)
Exercises
416(2)
Chapter Summary
418(3)
7 Generalized Eigenvectors
421(26)
7.1 Generalized Eigenvectors
421(10)
Exercises
429(2)
7.2 Chain Bases
431(16)
Jordan Form
438(5)
Exercises
443(1)
The Cayley-Hamilton Theorem
444(1)
Chapter Summary
445(2)
8 Numerical Techniques
447(44)
8.1 Condition Number
447(7)
Condition Number
449(3)
Least Squares
452(1)
Exercises
453(1)
8.2 Computing Eigenvalues
454(37)
Iteration
454(4)
The QR Method
458(6)
Exercises
464(1)
Chapter Summary
465(2)
Answers And Hints
467(24)
Index 491
RICHARD C. PENNEY, PHD is Emeritus Professor in the Department of Mathematics and former Director of the Mathematics/Statistics Actuarial Science Program at Purdue University. He has authored numerous journal articles, received several major teaching awards, and is an active researcher. He received his graduate education at MIT.