Construction of Multivector Inverse for Clifford Algebras Over $$2m+1$$2m+1-Dimensional Vector Spaces from Multivector Inverse for Clifford Algebras Over 2m-Dimensional Vector Spaces
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DOI: 10.1007/s00006-019-0942-7
Abstract: Assuming known algebraic expressions for multivector inverses in any Clifford algebra over an even dimensional vector space $$\mathbb {R}^{p',q'}$$Rp′,q′, $$n'=p'+q'=2m$$n′=p′+q′=2m, we derive a closed algebraic expression for the multivector inverse over vector spaces one dimension… read more here.
Keywords: vector spaces; multivector inverse; clifford algebras; dimensional vector ... See more keywords
On the Partial Hyperbolicity of Robustly Transitive Sets with Singularities
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DOI: 10.1007/s10884-022-10132-7
Abstract: Homoclinic tangencies and singular hyperbolicity are involved in the Palis conjecture for vector fields. Typical three dimensional vector fields are well understood by recent works. We study the dynamics of higher dimensional vector fields that… read more here.
Keywords: robustly transitive; homoclinic tangencies; dimensional vector; vector fields ... See more keywords
Structural inference in sparse high-dimensional vector autoregressions
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DOI: 10.1016/j.jeconom.2022.01.003
Abstract: We consider statistical inference for impulse responses in sparse, structural high-dimensional vector autoregressive (SVAR) systems. We introduce consistent estimators of impulse responses in the high-dimensional setting and suggest valid inference procedures for the same parameters.… read more here.
Keywords: structural inference; inference; dimensional vector; impulse responses ... See more keywords
Aspects of Differential Calculus Related to Infinite-Dimensional Vector Bundles and Poisson Vector Spaces
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DOI: 10.3390/axioms11050221
Abstract: We prove various results in infinite-dimensional differential calculus that relate the differentiability properties of functions and associated operator-valued functions (e.g., differentials). The results are applied in two areas: (1) in the theory of infinite-dimensional vector… read more here.
Keywords: differential calculus; vector bundles; dimensional vector; vector ... See more keywords
Products of Involutions of an Infinite-dimensional Vector Space
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DOI: 10.4153/s0008414x19000579
Abstract: We prove that every automorphism of an infinite-dimensional vector space over a field is the product of four involutions, a result that is optimal in the general case. We also characterize the automorphisms that are… read more here.
Keywords: dimensional vector; infinite dimensional; products involutions; vector space ... See more keywords
Statistical Inference for High-Dimensional Vector Autoregression with Measurement Error
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DOI: 10.5705/ss.202021.0151
Abstract: High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model. While there has… read more here.
Keywords: measurement error; autoregression measurement; inference; dimensional vector ... See more keywords