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Table of contents (10 chapters)
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About this book
A typical feature is where computational algorithms and theoretical proofs are brought together. Another is respect for symmetry, so that when this has some part in the form of a matter it should also be reflected in the treatment. Issues relating to computational method are covered. These interests may have suggested a limited account, to be rounded-out suitably. However this limitation where basic material is separated from further reaches of the subject has an appeal of its own.
To the `elementary operations' method of the textbooks for doing linear algebra, Albert Tucker added a method with his `pivot operation'. Here there is a more primitive method based on the `linear dependence table', and yet another based on `rank reduction'. The determinant is introduced in a completely unusual upside-down fashion where Cramer's rule comes first. Also dealt with is what is believed to be a completely new idea, of the `alternant', a function associated with the affine space the way the determinant is with the linear space, with n+1 vector arguments, as the determinant has n. Then for affine (or barycentric) coordinates we find a rule which is an unprecedented exact counterpart of Cramer's rule for linear coordinates, where the alternant takes on the role of the determinant. These are among the more distinct or spectacular items for possible novelty, or unfamiliarity. Others, with or without some remark, may be found scattered in different places.
Authors and Affiliations
Bibliographic Information
Book Title: Linear Dependence
Book Subtitle: Theory and Computation
Authors: S. N. Afriat
DOI: https://doi.org/10.1007/978-1-4615-4273-5
Publisher: Springer New York, NY
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media New York 2000
Hardcover ISBN: 978-0-306-46428-7Published: 30 September 2000
Softcover ISBN: 978-1-4613-6919-6Published: 23 October 2012
eBook ISBN: 978-1-4615-4273-5Published: 06 December 2012
Edition Number: 1
Number of Pages: XV, 175
Topics: Algebra, Numeric Computing, Applications of Mathematics, Theory of Computation, Linear and Multilinear Algebras, Matrix Theory