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APPLICATIONS OF SYSTEMS OF QUADRATIC FORMS TO GENERALISED QUADRATIC FORMS

open access: yesBulletin of the Australian Mathematical Society, 2020
A system of quadratic forms is associated to every generalised quadratic form over a division algebra with involution of the first kind in characteristic two. It is shown that this system determines the isotropy behaviour and the isometry class of generalised quadratic forms.
Nokhodkar, A. H.
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On quadratic differential forms

Proceedings of 1994 33rd IEEE Conference on Decision and Control, 1998
The authors develop a theory for linear time-invariant differential systems and quadratic functionals. It is shown that for systems described by one-variable polynomial matrices, the appropriate tool to express quadratic functionals of the system variables are two-variable polynomial matrices. The authors present a description of the interaction of one-
Willems, Jan C., Trentelman, Harry L.
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Abstract Quadratic Forms

Canadian Journal of Mathematics, 1969
We shall be studying the following structure, which we shall call a V-form (“Vector-valued form”). Let G and W be additive abelian groups with every element of order 2 (i.e. vector spaces over the field GF(2) of two elements). Let there be given a symmetric bilinear map from G × G to W; we shall write it simply as a product ab. We define an equivalence
Kaplansky, Irving, Shaker, Richard J.
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A note on quadratic forms

Mathematical Programming, 1999
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xin Chen, Ya-Xiang Yuan
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Representation by Quadratic Forms

The Annals of Mathematics, 1949
1. Introduction. The elementary portions of the theory of integral representation of numbers or forms by quadratic forms will be somewhat simplified and generalized in this article. This indicates certain directions in which new applications can be made.
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On the Theory of Quadratic Forms

The Annals of Mathematics, 1949
In this note we give an extention of the analytic theory of quadratic forms of C. L. Siegel'. We use the well-known matrix notation, if the contrary is not expressly mentioned we suppose the elements of all matrices to be rational integers. Let A(S, T; P, v) denote the number of solutions X of the Diophantic matrix equation X'SX = T, which satisfy the ...
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DISTRIBUTIONS OF QUADRATIC FORMS

Australian Journal of Statistics, 1988
summaryExact expressions for the distribution function of a random variable of the form c1χ2m+c2χ2n are given where χ2m and χ2nχ2n are independent chi‐square random variables with m and n degrees of freedom respectively. (The positive ci are distinct).
Bock, Mary Ellen, Solomon, Herbert
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