The affine group I. Bruhat decomposition
نویسندگان
چکیده
منابع مشابه
Fast Generalized Bruhat Decomposition
The deterministic recursive pivot-free algorithms for the computation of generalized Bruhat decomposition of the matrix in the field and for the computation of the inverse matrix are presented. This method has the same complexity as algorithm of matrix multiplication and it is suitable for the parallel computer systems.
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Deterministic recursive algorithms for the computation of generalized Bruhat decomposition of the matrix in commutative domain are presented. This method has the same complexity as the algorithm of matrix multiplication.
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For our first example, consider V = Cn. Let {e1, . . . en} be the standard basis of Cn, and fix the full flag F• = 0 ⊂ 〈e1〉 ⊂ 〈e1, e2〉 ⊂ · · · ⊂ 〈e1, . . . , en−1〉 ⊂ V Note that any other flag can be obtained from this one by acting with an element of GLn(C). Specifically, any flag V• = 0 ⊂ V1 ⊂ · · · ⊂ Vn = V in Cn has the form V• = 0 ⊂ 〈ge1〉 ⊂ 〈ge1, ge2〉 ⊂ · · · ⊂ 〈ge1, . . . , gen〉 = V for s...
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In this paper we improve the layered implementation of arbitrary stabilizer circuits introduced by Aaronson and Gottesman in Phys. Rev. A 70(052328), 2004: to implement a general stabilizer circuit, we reduce their 11-stage computation -HC-P-C-P-C-H-P-C-P-Cover the gate set consisting of Hadamard, Controlled-NOT, and Phase gates, into a 7-stage computation of the form -C-CZ-P-H-P-CZ-C-. We show...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1972
ISSN: 0021-8693
DOI: 10.1016/0021-8693(72)90071-3