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Quadratic Forms in Infinite Dimensional Vector Spaces (Paperback, 1979 ed.)
Loot Price: R1,544
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Quadratic Forms in Infinite Dimensional Vector Spaces (Paperback, 1979 ed.)
Series: Progress in Mathematics, 1
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For about a decade I have made an effort to study quadratic forms
in infinite dimensional vector spaces over arbitrary division
rings. Here we present in a systematic fashion half of the results
found du ring this period, to wit, the results on denumerably
infinite spaces (" ~O- forms") . Certain among the resul ts
included here had of course been published at the time when they
were found, others appear for the first time (the case, for
example, in Chapters IX, X, XII where I in clude results contained
in the Ph.D.theses by my students w. Allenspach, L. Brand, U.
Schneider, M. Studer). If one wants to give an introduction to the
geometric algebra of infinite dimensional quadratic spaces, a
discussion of ~ -dimensional 0 spaces ideally serves the purpose.
First, these spaces show a large nurober of phenomena typical of
infinite dimensional spaces. Second, most proofs can be done by
recursion which resembles the familiar pro cedure by induction in
the finite dimensional Situation. Third, the student acquires a
good feeling for the linear algebra in infinite di mensions because
it is impossible to camouflage problems by topological expedients
(in dimension ~O it is easy to see, in a given case, wheth er
topological language is appropriate or not) .
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