On the other hand, we have increased the amount of material in the text, so that it can be used for a rather comprehensive one-year course in linear algebra and even as a reference book for mathematicians. The major changes have been in our treatments of canonical forms and inner product spaces. In Chapter 6 we no longer begin with the general spatial theory which underlies the theory of canonical forms. We first handle characteristic values in relation to triangulation and diagonalization theorems and then build our way up to the general theory.
We have split Chapter 8 so that the basic material on inner product spaces and unitary diagonalization is followed by a Chapter 9 which treats sesqui-linear forms and the more sophisticated properties of normal opera- tors, including normal operators on real inner product spaces. We have also made a number of small changes and improvements from the first edition.
But the basic philosophy behind the text is unchanged. We have made no particular concession to the fact that the majority of the students may not be primarily interested in mathematics.
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For we believe a mathe- matics course should not give science, engineering, or social science students a hodgepodge of techniques, but should provide them with an understanding of basic mathematical concepts. For this reason, we have avoided the introduction of too many abstract ideas at the very beginning of the book. In addition, we have included an Appendix which presents such basic ideas as set, function, and equivalence relation.
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We have found it most profitable not to dwell on these ideas independently, but to advise the students to read the Appendix when these ideas arise. Throughout the book we have included a great variety of examples of the important concepts which occur. The study of such examples is of fundamental importance and tends to minimize the number of students who can repeat defini- tion, theorem, proof in logical order without grasping the meaning of the abstract concepts.
The book also contains a wide variety of graded exercises about six hundred , ranging from routine applications to ones which will extend the very best students. These exercises are intended to be an important part of the text.
ISBN 13: 9780135367971
Chapter 1 deals with systems of linear equations and their solution by means of elementary row operations on matrices. It has been our practice to spend about six lectures on this material. It provides the student with some picture of the origins of linear algebra and with the computational technique necessary to under- stand examples of the more abstract ideas occurring in the later chapters.
Chap- ter 2 deals with vector spaces, subspaces, bases, and dimension. Chapter 3 treats linear transformations, their algebra, their representation by matrices, as well as isomorphism, linear functionals, and dual spaces. He received is B. Professor Adams's research interests focus on differential equations, especially in applications to biology and physics, and he has published another textbook, Measure Theory and Probability , with Victor Guillemin.
Outside of the university, he enjoys running, traveling, and hiking with his wife and three children. Your way. Find your Rep. Linear Algebra: A Geometric Approach, Second Edition , presents the standard computational aspects of linear algebra and includes a variety of intriguing interesting applications that would be interesting to motivate science and engineering students, as well as help mathematics students make t Students - Buy or Rent. Read and study old-school with our bound texts. Rent 3 months. Rent 4 months.
Rent 6 months. Rent 1 year. Home Features New to This Edition. Geometry is introduced early , using vector algebra to do analytic geometry in the first section and dot product in the second.
Concepts and understanding is emphasized, doing proofs in text and providing plenty of exercises. To aid the student in adjusting to the mathematical rigor, blue boxes are provided which discuss matters of logic and proof technique or advice on formulating problem-solving strategies. Rotations, reflections, and projections are used as a first brush with the notion of linear transformation when introducing matrix multiplication. Linear transformations are then treated in concert with the discussion of projections. Thus, the change-of-basis formula is motivated by starting with a coordinate system in which a geometrically defined linear transformation is clearly understood and asking for its standard matrix.
Orthogonal complements are emphasized, with their role in finding a homogenous system of linear equations that defines a given subspace of Rn. New to This Edition. New to Chapter 3, Vector Spaces: streamlined treatment of four fundamental subspaces and clarified coverage of linear independence and basis.
Updated and reorganized Chapters 4, Projections and Linear Transformations, and 5, Determinants with improved clarity in the coverage of Change of Basis and the geometric material. Stronger emphasis throughout on key concepts and understanding, through new proofs and a variety of text exercises. New Blue Boxes , integrated throughout the text, discuss matters of logic and proof techniques or advice on formulating problem-solving strategies to aid the student in adjusting to the mathematical rigor. Digital Options. Table of Contents. Chapter 1. Vectors and Matrices 1. Vectors 2.
Elementary Linear Algebra 2nd Edition | Mathematics | Science
Dot Product 3. Systems of Linear Equations and Gaussian Elimination 5. The Theory of Linear Systems 6. Some Applications. Chapter 2. Matrix Algebra 1. Matrix Operations 2.
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