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A-bilinear forms and generalised A-quadratic forms on unitary left A-modules

Published online by Cambridge University Press:  17 April 2009

C.-S. Lin
C.-S. Lin
Affiliation:
Mathematics Department, Bishop's University, Lennoxville, Quebec, Cananda. J1M 1Z7
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Abstract

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In this paper we shall define a generalised A-quadratic form and prove that in some way this form and an A-bilinear form are equivalent to each other. Our result characterises that of Vukman in the sense that we use any n vectors for a fixed n ≥ 2, instead of any two vectors. Consequently, a new generalisation of an inner product space among vector spaces is obtained. This also leads to a new relationship between a 2-inner product space and a 2-normed space.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 39 , Issue 1 , February 1989 , pp. 49 - 58
Copyright
Copyright © Australian Mathematical Society 1989

References

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