Hostname: page-component-745bb68f8f-cphqk Total loading time: 0 Render date: 2025-01-12T15:37:51.897Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Gram Matrix

Published online by Cambridge University Press:  20 November 2018

Israel Halperin
Israel Halperin*
Affiliation:
Queen's University Kingston, Canada
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The material sketched here is mostly well known and concerns the geometrical inter-relations of vectors in a Hilbert (that is, complete inner product) space. The discussion and references are (obviously) not exhaustive but I hope the reader will find here some interesting problems.

We shall permit the scalars to be real, complex or quaternionic numbers. The inner product of vectors x and y will be denoted (x|y).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 5 , Issue 3 , September 1962 , pp. 265 - 280
Copyright
Copyright © Canadian Mathematical Society 1962

References

1. Bourbaki, N., Algébre, Ch. 9, §7.Google Scholar
2. Courant, R. and Hilbert, D., Methoden der Mathematischen Physik, vol. 1 (Springer, Berlin, 1931).Google Scholar
3. Dieudonné, J., Les determinants sur un c o r p s non commutatif, Bull. Soc. Math. France, vol. 71 (1943), pp. 27-45.Google Scholar
4. John, von Neumann, Functional Operators, vol. II: The Geometry of Orthogonal Spaces, Annals of Mathematics Studies, No. 22, Princeton, 1950.Google Scholar
5. Stone, M. H., Linear Transformations in Hilbert Space, American Mathematical Society Colloquium Publications Vol. XV, New York, 1932.Google Scholar
6. Teichmuller, O., Operatoren im Wachsschen Raum, J. Reine and Angew. Math., vol. 174(1935), pp. 73-124.Google Scholar