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On quadratic differential forms
Proceedings of 1994 33rd IEEE Conference on Decision and Control, 1998The 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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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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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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Proceedings of the London Mathematical Society, 1987
Let Q be a quadratic form, \(Q=L^ 2_ 1+... +L^ 2_ r-... -L^ 2_ n\) where \(L_ 1,...,L_ n\) are real linearly independent quadratic forms. If \(n=18\), \(r=9\); \(n=19\), \(8\leq r\leq 11\); or \(n=20\), \(7\leq r\leq 13\), then we can solve \(| Q(x)| 0\). This extends work of Davenport, Birch and Ridout.
Baker, R. C., Schlickewei, H. P.
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Let Q be a quadratic form, \(Q=L^ 2_ 1+... +L^ 2_ r-... -L^ 2_ n\) where \(L_ 1,...,L_ n\) are real linearly independent quadratic forms. If \(n=18\), \(r=9\); \(n=19\), \(8\leq r\leq 11\); or \(n=20\), \(7\leq r\leq 13\), then we can solve \(| Q(x)| 0\). This extends work of Davenport, Birch and Ridout.
Baker, R. C., Schlickewei, H. P.
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Canadian Journal of Mathematics, 1983
0. Introduction. Simplicial quadratic forms (cf. Definition 1.4), and various equivalent forms, have occasionally been studied in geometry [8], and in number theory [9], [10], in connection with the extremal properties of integral quadratic forms. Our investigations, which employ simple techniques from graph theory and geometry, partly continue both ...
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0. Introduction. Simplicial quadratic forms (cf. Definition 1.4), and various equivalent forms, have occasionally been studied in geometry [8], and in number theory [9], [10], in connection with the extremal properties of integral quadratic forms. Our investigations, which employ simple techniques from graph theory and geometry, partly continue both ...
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Canadian Journal of Mathematics, 1952
Hermite [4] in the course of his investigations on the transformation theory of abelian functions, introduced the notion of abelian quadratic forms. They are quadratic forms whose matrices of orders 2n, satisfywhere k ≠ 0 is a real number, and is the unit matrix of order n.
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Hermite [4] in the course of his investigations on the transformation theory of abelian functions, introduced the notion of abelian quadratic forms. They are quadratic forms whose matrices of orders 2n, satisfywhere k ≠ 0 is a real number, and is the unit matrix of order n.
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Proceedings of the London Mathematical Society, 1959
Davenport, Harold, Ridout, D.
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Davenport, Harold, Ridout, D.
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2017
This chapter presents a few standard definitions and results about quadratic forms and polar spaces. It begins by defining a quadratic module and a quadratic space and proceeds by discussing a hyperbolic quadratic module and a hyperbolic quadratic space.
Bernhard M¨uhlherr +2 more
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This chapter presents a few standard definitions and results about quadratic forms and polar spaces. It begins by defining a quadratic module and a quadratic space and proceeds by discussing a hyperbolic quadratic module and a hyperbolic quadratic space.
Bernhard M¨uhlherr +2 more
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