منابع مشابه
An involutory Pascal matrix
An involutory upper triangular Pascal matrix Un is investigated. Eigenvectors of Un and of UT n are considered. A characterization of Un is obtained, and it is shown how the results can be extended to matrices over a commutative ring with unity. © 2004 Elsevier Inc. All rights reserved.
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For any matrix X let X′ denote its transpose. It is known that if A is an n-by-n matrix over a field F , then A and A′ are congruent over F , i.e., XAX′ = A′ for some X ∈ GLn(F ). Moreover, X can be chosen so that X2 = In, where In is the identity matrix. An algorithm is constructed to compute such an X for a given matrix A. Consequently, a new and completely elementary proof of that result is ...
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In this paper, we derive a family of fast and stable algorithms for multiplying and inverting n × n Pascal matrices that run in O(n log n) time and are closely related to De Casteljau’s algorithm for Bézier curve evaluation. These algorithms use a recursive factorization of the triangular Pascal matrices and improve upon the cripplingly unstable O(n log n) fast Fourier transform-based algorithm...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2004
ISSN: 0024-3795
DOI: 10.1016/j.laa.2004.02.027