Representation of Quadratic forms
نویسنده
چکیده
منابع مشابه
Approximating the Distributions of Singular Quadratic Expressions and their Ratios
Noncentral indefinite quadratic expressions in possibly non- singular normal vectors are represented in terms of the difference of two positive definite quadratic forms and an independently distributed linear combination of standard normal random variables. This result also ap- plies to quadratic forms in singular normal vectors for which no general representation is currently available. The ...
متن کاملApplications of quadratic D-forms to generalized quadratic forms
In this paper, we study generalized quadratic forms over a division algebra with involution of the first kind in characteristic two. For this, we associate to every generalized quadratic from a quadratic form on its underlying vector space. It is shown that this form determines the isotropy behavior and the isometry class of generalized quadratic forms.
متن کاملSome Probability Inequalities for Quadratic Forms of Negatively Dependent Subgaussian Random Variables
In this paper, we obtain the upper exponential bounds for the tail probabilities of the quadratic forms for negatively dependent subgaussian random variables. In particular the law of iterated logarithm for quadratic forms of independent subgaussian random variables is generalized to the case of negatively dependent subgaussian random variables.
متن کاملTHUE-VINOGRADOV AND INTEGERS OF THE FORM x +Dy
Introduction – Study of an Elementary Proof 1 1. The Lemmas of Thue and Vinogradov 4 2. Preliminaries on Quadratic Reciprocity and Quadratic Forms 4 2.1. Quadratic reciprocity law 4 2.2. Binary quadratic forms 5 3. Thue-Vinogradov Applied to Binary Quadratic Forms 7 4. First Applications of Theorem 9 8 4.1. Indefinite forms 8 4.2. Positive definite forms 10 5. Primes of the form x +Dy for idone...
متن کاملOn the solving matrix equations by using the spectral representation
The purpose of this paper is to solve two types of Lyapunov equations and quadratic matrix equations by using the spectral representation. We focus on solving Lyapunov equations $AX+XA^*=C$ and $AX+XA^{T}=-bb^{T}$ for $A, X in mathbb{C}^{n times n}$ and $b in mathbb{C} ^{n times s}$ with $s < n$, which $X$ is unknown matrix. Also, we suggest the new method for solving quadratic matri...
متن کاملAlgorithms for quadratic forms
We present algorithms for square classes, quadratic forms and Witt classes of quadratic forms over the eld of rational functions of one variable over the reals. The algorithms are capable of: nding the unique representative of a square class, deciding if a given function is a square or a sum of squares and deciding if a quadratic form is isotropic or hyperbolic. Moreover we propose a representa...
متن کامل