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Quadratic Forms
"... In time series analysis, tests for serial independence, symmetry, and goodnessoffit based on divergence measures, such as the KullbackLeibler divergence or Hellinger distance are currently receiving much interest. We consider replacing the divergence measures in these tests by kernelbased quadrat ..."
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based quadratic form. In this way we avoid the common practice of using plugin estimators. Our approach separates the problem of consistent estimation of the divergence measure from that of estimating the underlying joint densities consistently. We construct a test for serial independence on the basis
Classification of quadratic forms
, 2011
"... We present the classification of quadratic forms over the rationals and then describe a partial classification of quadratic forms over Z/mZ, when 4 ̸ m. ..."
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We present the classification of quadratic forms over the rationals and then describe a partial classification of quadratic forms over Z/mZ, when 4 ̸ m.
Distributions of quadratic forms
"... A well known fact is that when testing hypotheses for covariance matrices, distributions of quadratic forms arise. A generalization of the distribution of the multivariate quadratic form XAX ′ , where X is a (p × n) normally distributed matrix and A is a (n × n) symmetric real matrix, is presented. ..."
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A well known fact is that when testing hypotheses for covariance matrices, distributions of quadratic forms arise. A generalization of the distribution of the multivariate quadratic form XAX ′ , where X is a (p × n) normally distributed matrix and A is a (n × n) symmetric real matrix, is presented
DECOMPOSABLE QUADRATIC FORMS AND INVOLUTIONS
"... Abstract. In his book on compositions of quadratic forms, Shapiro asks whether a quadratic form decomposes as a tensor product of quadratic forms when its adjoint involution decomposes as a tensor product of involutions on central simple algebras. We give a positive answer for quadratic forms define ..."
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Abstract. In his book on compositions of quadratic forms, Shapiro asks whether a quadratic form decomposes as a tensor product of quadratic forms when its adjoint involution decomposes as a tensor product of involutions on central simple algebras. We give a positive answer for quadratic forms
Quadratic Form Expansions for Unitaries
"... Abstract. We introduce techniques to analyze unitary operations in terms of quadratic form expansions, a form similar to a sum over paths in the computational basis when the phase contributed by each path is described by a quadratic form over R. We show how to relate such a form to an entangled reso ..."
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Abstract. We introduce techniques to analyze unitary operations in terms of quadratic form expansions, a form similar to a sum over paths in the computational basis when the phase contributed by each path is described by a quadratic form over R. We show how to relate such a form to an entangled
More on Distributions of Quadratic Forms
"... A generalization of the distribution of the multivariate quadratic form XAX ′, where X is a (p × n) normally distributed matrix and A is a (n × n) symmetric real matrix, is presented. We show that the distribution of the quadratic form is the same as the distribution of a weighted sum of noncentral ..."
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A generalization of the distribution of the multivariate quadratic form XAX ′, where X is a (p × n) normally distributed matrix and A is a (n × n) symmetric real matrix, is presented. We show that the distribution of the quadratic form is the same as the distribution of a weighted sum of noncentral
On the Pfister Number of Quadratic Forms
"... Abstract. The generic quadratic form of even dimension n with trivial discriminant over an arbitrary field of characteristic different from 2 containing a square root of −1 can be written in the Witt ring as a sum of 2fold Pfister forms using n − 2 terms and not less. The number of 2fold Pfister f ..."
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Abstract. The generic quadratic form of even dimension n with trivial discriminant over an arbitrary field of characteristic different from 2 containing a square root of −1 can be written in the Witt ring as a sum of 2fold Pfister forms using n − 2 terms and not less. The number of 2fold Pfister
Finiteness theorems for quadratic forms
"... The classical “Four Squares Theorem” of Lagrange (1770) asserts that any positive integer can be expressed as the sum of four squares—that is, the quadratic form x2 + y2 + z2 + t2 represents all (positive) integers. When does a general (positive definite) quadratic form represent all (positive) int ..."
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The classical “Four Squares Theorem” of Lagrange (1770) asserts that any positive integer can be expressed as the sum of four squares—that is, the quadratic form x2 + y2 + z2 + t2 represents all (positive) integers. When does a general (positive definite) quadratic form represent all (positive
On the degeneracy of quadratic forms
, 2012
"... Have you encountered this problem: Given a quadratic form, is it a product of two linear forms? The problem has a simple solution, and was solved several centuries ago. However, many people we talked to found it interesting and were surprised they had ..."
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Have you encountered this problem: Given a quadratic form, is it a product of two linear forms? The problem has a simple solution, and was solved several centuries ago. However, many people we talked to found it interesting and were surprised they had
Results 1  10
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