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Books > Science & Mathematics > Mathematics > Algebra
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Linear Dependence - Theory and Computation (Hardcover, 2000 ed.)
Loot Price: R1,510
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Linear Dependence - Theory and Computation (Hardcover, 2000 ed.)
Expected to ship within 10 - 17 working days
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Deals with the most basic notion of linear algebra, to bring
emphasis on approaches to the topic serving at the elementary level
and more broadly. 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.
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