Linear Algebra With Applications
| Date: 06 May 2011, 00:42
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This successful text is an introduction to the basic ideas and techniques of linear algebra for first- or second-year students who have a working knowledge of high school algebra (calculus is not a prerequisite). The author maintains a balance among the computational skills, theory, and applications of linear algebra--while keeping the level suitable for beginning students--and offers a multitude of examples and exercises to help students master the material.
Taking a traditional approach to the subject of Linear Algebra, with some introduction for students to R^n, the Fourth Edition of Linear Algebra with Applications, newly acquired by McGraw-Hill, continues the tradition of accuracy and excellence associated with W. Keith Nicholson. Unlike the previous edition, however, the Fourth Edition introduces eigenvalues early on, in chapter 3, in a rigorous way using only matrix algebra and determinants. As well, Nicholson has added a new "bridging" chapter from Vector Geometry (Chapter 4) to the notion of an Abstract Vector Space (Chapter 6). In the traditional manner, Nicholson 4/e allows students to "hit the wall" with theory, but, with these new features, also provides students with the tools needed to overcome the wall.
Synopsis
This text achieves a balance among computational skills, theories and applications of linear algebra. The contents can be arranged to allow for the presentation of a traditional introduction to linear algebra or a more applied course. More than 330 solved examples are included; many are computational and devoted to applications. This edition leans towards matrix computations and applications, and has a much less abstract focus than the second edition. This fifth edition has been updated to include: emphasis on more matrix computation with a corresponding lowering of the level of absraction; new exercises and examples; new sections on positive definitive matrices and the block upper triangular form of a matrix; sections on Gaussian elimination and vector geometry; Eigenvalues and diagonalization with applications moved earlier in text (chapter 6); removal of chapter 9 with discussion of operators being divided between chapters 7 and 8; biographical footnotes.
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