Results 161 to 170 of about 535 (196)
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Linear Forms and Bilinear Forms
2015In this chapter we study different classes of maps between one or two K-vector spaces and the one dimensional K-vector space defined by the field K itself. These maps play an important role in many areas of Mathematics, including Analysis, Functional Analysis and the solution of differential equations.
Jörg Liesen, Volker Mehrmann
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2021
Assume that in a n-dimensional vector space Ln a basis B = (e1, e2, …, en) is specified. Consider two vectors belonging to the space Ln: $$\displaystyle \boldsymbol {x}=\sum _{i=1}^n x_i \boldsymbol {e}_i,\quad \boldsymbol {y}=\sum _{i=1}^n y_i \boldsymbol {e}_i, $$ where \(x_i,y_i\in \mathbb {R}\) for all i = 1, 2, …, n.
Sergei Kurgalin, Sergei Borzunov
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Assume that in a n-dimensional vector space Ln a basis B = (e1, e2, …, en) is specified. Consider two vectors belonging to the space Ln: $$\displaystyle \boldsymbol {x}=\sum _{i=1}^n x_i \boldsymbol {e}_i,\quad \boldsymbol {y}=\sum _{i=1}^n y_i \boldsymbol {e}_i, $$ where \(x_i,y_i\in \mathbb {R}\) for all i = 1, 2, …, n.
Sergei Kurgalin, Sergei Borzunov
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Bilinear transformations and forms
1995Bilinear transformations and bilinear forms are introduced and studied. Their matrix representation, and especially the representation of symmetric bilinear forms, is presented. Orthogonality relative to a bilinear form is considered. These notions are then used to define the tensor product of vector spaces, and the properties of the tensor product are
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BILINEAR FORMS AND LINEAR CODES
Acta Mathematica Scientia, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2002
In this chapter we shall apply some of the previous results in a study of certain types of linear forms.
T. S. Blyth, E. F. Robertson
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In this chapter we shall apply some of the previous results in a study of certain types of linear forms.
T. S. Blyth, E. F. Robertson
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2013
In this chapter, we describe the foundations of the theory of non-degenerate symmetric bilinear forms on finite-dimensional vector spaces and their orthogonal groups. Among the highlights of this discussion are the Cartan–Dieudonne Theorem, which states that any orthogonal transformation is a finite product of reflections, and Witt’s Theorem giving a ...
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In this chapter, we describe the foundations of the theory of non-degenerate symmetric bilinear forms on finite-dimensional vector spaces and their orthogonal groups. Among the highlights of this discussion are the Cartan–Dieudonne Theorem, which states that any orthogonal transformation is a finite product of reflections, and Witt’s Theorem giving a ...
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Journal of Mathematical Sciences, 1999
The author studies bilinear forms on additive categories and reproves some of the results obtained by \textit{H.-G. Quebbemann, W. Scharlau} and \textit{M. Schulte} in ``Quadratic and hermitian forms in additive and abelian categories'' [J. Algebra 59, 264-289 (1979; Zbl 0412.18016)], a paper, of which the author seems to be completely unaware.
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The author studies bilinear forms on additive categories and reproves some of the results obtained by \textit{H.-G. Quebbemann, W. Scharlau} and \textit{M. Schulte} in ``Quadratic and hermitian forms in additive and abelian categories'' [J. Algebra 59, 264-289 (1979; Zbl 0412.18016)], a paper, of which the author seems to be completely unaware.
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2013
The theory of bilinear form and quadratic form is used [5] in the analytic geometry for getting the classification of the conics and of the quadrics.
George A. Anastassiou, Iuliana F. Iatan
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The theory of bilinear form and quadratic form is used [5] in the analytic geometry for getting the classification of the conics and of the quadrics.
George A. Anastassiou, Iuliana F. Iatan
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