Linear Algebra

Richard C. Penney 지음

Wiley 2020년 12월 08일 출간 국내도서 : 2021년 10월 01일 출간

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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 cour

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1 Systems of Linear Equations 1 1.1 The Vector Space of m × n Matrices 1 The Space R n 4 Linear Combinations and Linear Dependence 6 What Is a Vector Space? 10 Exercises 16 1.1.1 Computer Projects/Exercises/Exercises 21 Introduction to MATLAB 21 1.1.2 Applications to Graph Theory I 24 Exercises 26 1.2 Systems 27 Rank: The Maximum Number of Linearly Independent Equations 33 Exercises 37 1.2.1 Computer Projects/Exercises 39 The Translation Theorem 39 1.2.2 Applications to Circuit Theory 40 Exercises 44 1.3 Gaussian Elimination 45 Spanning in Polynomial Spaces 56 Computational Issues: Pivoting 59 Exercises 60 Computational Issues: Flops 65 1.3.1 Computer Projects/Exercises 66 Using tolerances in rref and rank 66 1.3.2 Applications to Traffic Flow 69 Exercises 70 1.4 Column Space and Nullspace 71 Subspaces 73 Exercises 82 1.4.1 Computer Projects/Exercises 90 The null Command 90 Chapter Summary 92 2 Linear Independence and Dimension 93 2.1 The Test for Linear Independence 93 Bases for the Column Space 99 Testing Functions for Independence 102 Exercises 104 2.1.1 Computer Projects/Exercises 108 Changing Pivot Columns 108 2.2 Dimension 109 Exercises 118 2.2.1 Computer Projects/Exercises 124 2.2.2 Applications to Differential Equations 125 Exercises 128 2.3 Row Space and the rank-nullity theorem 128 Bases for the Row Space 130 Computational Issues: Computing Rank 138 Exercises 140 2.3.1 Computer Projects/Exercises 144 Random Matrices of a given Rank 144 Chapter Summary 145 3 Linear Transformations 147 3.1 The Linearity Properties 147 Exercises 154 3.1.1 Computer Projects/Exercises 159 2-D Comp

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저자(글) Richard C. Penney

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.