W. Keith Nicholson's "Linear Algebra with Applications, Fifth Canadian Edition" is written for first and second year students at both the college or university level. Its real world approach challenges students step-by-step, gradually bringing them to a higher level of understanding from abstract to more general concepts. Real world applications have been added to the new edition, including: Directed graphs; Google PageRank; Computer graphics; Correlation and Variance; and Finite Fields and Linear Codes.In addition to the new applications, the author offers several new exercises and examples throughout each chapter. Some new examples include: motivating matrix multiplication (Chapter 2) and a new way to expand a linearly independent set to a basis using an existing basis. While some instructors will use the text for one semester, ending at Chapter 5 The Vector Space Rn others will continue with more abstract concepts being introduced. Chapter 5 prepares students for the transition, acting as the "bridging" chapter, allowing challenging concepts like subspaces, spanning, independence and dimension to be assimilated first in the concrete context of Rn.
This "bridging" concept eases students into the introduction of vector spaces in Chapter 6.
Auflage
Sprache
Verlagsort
Verlagsgruppe
McGraw-Hill Education - Europe
Zielgruppe
Für höhere Schule und Studium
Maße
Höhe: 249 mm
Breite: 206 mm
Dicke: 25 mm
Gewicht
ISBN-13
978-0-07-092277-8 (9780070922778)
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Schweitzer Klassifikation
Dr. W. Keith Nicholson earned his undergraduate Degree in Applied Mathematics at the University of Alberta, and received his Ph.D. in Pure Mathematics from the University of California at Santa Barbara in 1970. He then moved to the University of Calgary, and has been a professor in the Department of Mathematics and Statistics since 1979, where he has been carrying out research in a branch of algebra called "Ring Theory". His continuing interest in teaching undergraduate students has led to another book in Linear Algebra (now in its third edition), a text in Abstract Algebra (second edition), and the creation (with Professor Claude Laflamme), of an internet tutorial for Linear Algebra called ILAW (Interactive Linear Algebra on the Web). Keith is married and has two grown sons.
Chapter 1 Systems of Linear Equations1.1 Solutions and Elementary Operations1.2 Gaussian Elimination1.3 Homogeneous Equations1.4 An Application to Network Flow1.5 An Application to Electrical Networks1.6 An Application to Chemical ReactionsSupplementary Exercises for Chapter 1Chapter 2 Matrix Algebra2.1 Matrix Addition, Scalar Multiplication, and Transposition2.2 Matrix Multiplication2.3 Matrix Inverses2.4 Elementary Matrices2.5 Matrix Transformations2.6 LU-Factorization</4>2.7 An Application to Input-Output Economic Models2.8 An Application to Markov ChainsSupplementary Exercises for Chapter 2Chapter 3 Determinants and Diagonalization3.1 The Cofactor Expansion3.2 Determinants and Matrix Inverses3.3 Diagonalization and Eigenvalues3.5 An Application to Linear Recurrences3.6 An Application to Population Growth3.7 Proof of the Cofactor ExpansionSupplementary Exercises for Chapter 3Chapter 4 Vector Geometry4.1 Vectors and Lines4.2 Projections and Planes4.3 The Cross Product4.4 Matrix Transformations II4.5 An Application to Computer GraphicsSupplementary Exercises for Chapter 4Chapter 5 The Vector Space Rn5.1 Subspaces and Spanning5.2 Independence and Dimension5.3 Orthogonality5.4 Rank of a Matrix5.5 Similarity and Diagonalization5.6 An Application to Correlation and Variance5.7 An Application to Least Squares ApproximationSupplementary Exercises for Chapter 5Chapter 6 Vector Spaces6.1 Examples and Basic Properties6.2 Subspaces and Spanning Sets6.3 Linear Independence and Dimension6.4 Finite Dimensional Spaces6.5 An Application to Polynomials6.6 An Application to Differential EquationsSupplementary Exercises for Chapter 6Chapter 7 Linear Transformations7.1 Examples and Elementary Properties7.2 Kernel and Image of a Linear Transformation7.3 Isomorphisms and Composition7.4 More on Linear RecurrencesChapter 8 Orthogonality8.1 Orthogonal Complements and Projections8.2 Orthogonal Diagonalization8.3 Positive Definite Matrices8.4 QR-Factorization8.5 Computing Eigenvalues8.6 Complex Matrices8.7 Best Approximation and Least Squares8.8 Finite Fields and Linear Codes8.9 An Application to Quadratic Forms8.10 An Application to Systems of Differential EquationsChapter 9 Change of Basis9.1 The Matrix of a Linear Transformation9.2 Operators and Similarity9.3 Invariant Subspaces and Direct Sums9.4 Block Triangular Form*9.5 Jordan Canonical FormChapter 10 Inner Product Spaces10.1 Inner Products and Norms10.2 Orthogonal Sets of Vectors10.3 Orthogonal Diagonalization10.4 Isometries10.5 An Application to Fourier Approximation
