Quadratic Forms in Infinite Dimensional Vector Spaces - Gross H.
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 (" NO-forms'''). Certain among the results 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 N-dimensional O spaces ideally serves the purpose. First, these spaces show a large number 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 NO it is easy to see, in a given case, wheth er topological language is appropriate or not).
EAN: 9780817611118Potrzebujesz pomocy? Masz pytania?Zadaj pytanie a my odpowiemy niezwłocznie, najciekawsze pytania i odpowiedzi publikując dla innych. 
