Zobrazeno 1 - 10
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pro vyhledávání: '"William C. Waterhouse"'
Carl Friedrich Gauss's textbook, Disquisitiones arithmeticae, published in 1801 (Latin), remains to this day a true masterpiece of mathematical examination..
Autor:
William C. Waterhouse
Publikováno v:
Linear Algebra and its Applications. 438:7-9
Every real ( 2 n + 1 ) × ( 2 n + 1 ) matrix can be written as a sum of a scalar, a skew matrix, and a matrix of rank ≤ n . For n = 1 , this proves a claim first stated in 1920, and the summands there are (nearly) unique.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9f249accab43cabde80a02fd62a1c10d
https://doi.org/10.1016/j.laa.2012.07.003
https://doi.org/10.1016/j.laa.2012.07.003
Autor:
William C. Waterhouse
Publikováno v:
Linear Algebra and its Applications. 392:39-44
Given a polynomial in characteristic p, the algorithm here will (without factorization) find a separable polynomial with the same irreducible factors or prove that none exists. This is what is needed to compute the Jordan decomposition of a matrix in
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a3090174c21dd1a9998ba969b5117d98
Autor:
William C. Waterhouse
Publikováno v:
Finite Fields and Their Applications. 9:135-139
For a d×d matrix over a finite field with q elements, the portion of d-tuples generating maximal cyclic subspaces is at least e−2log(q)/[log(q)+log(d)], and there are examples of that order of magnitude.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f341de82e94d673bc7dcf8e19b674338
https://doi.org/10.1016/s1071-5797(02)00015-1
https://doi.org/10.1016/s1071-5797(02)00015-1
Autor:
William C. Waterhouse
Publikováno v:
Linear Algebra and its Applications. 323:99-104
For a projective plane over a field F , we classify all asymmetric linear correlations up to equivalence under the group of all collineations. The result is derived from the finer equivalence of bilinear forms on three-dimensional spaces.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bce306c564e74a6f541ef2fdc03f8e7a
https://doi.org/10.1016/s0024-3795(00)00248-2
https://doi.org/10.1016/s0024-3795(00)00248-2
Autor:
William C. Waterhouse
Publikováno v:
Archiv der Mathematik. 82:298-300
Let F be a field finite-dimensional over subfields A and B. It is known from Galois theory that the degree \( [F : A \cap B] \) can be infinite. If F is purely inseparable over B and finitely generated over the prime field, this cannot happen; but it
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::12ded2327d9696e9fb8efd55e5da8830
https://doi.org/10.1007/s00013-003-4872-0
https://doi.org/10.1007/s00013-003-4872-0
Autor:
William C. Waterhouse
Publikováno v:
Linear Algebra and its Applications. 231:175-179
The trace takes bilinear forms over a separable field extension to certain bilinear forms over the base field. This paper shows how to compute the inverse of that process. The construction implies that two known ways of classifying rational symmetric
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::22a02d63e4ef4d101d3184b41b388ea1
https://doi.org/10.1016/0024-3795(95)90018-7
https://doi.org/10.1016/0024-3795(95)90018-7
Autor:
William C. Waterhouse
Publikováno v:
Journal of Algebra. 173:271-280
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d680e5cee413d8fc9682e3ca3b4a037e
https://doi.org/10.1006/jabr.1995.1088
https://doi.org/10.1006/jabr.1995.1088
Autor:
William C. Waterhouse
Publikováno v:
Finite Fields and Their Applications. 1:57-63
Call matrices A and B congruent when PAPt = B for some invertible P. Extending a result of Gow, this paper shows that the number of congruence classes in the n × n matrices over Fq is the coefficient of tn in [formula] (where e = 1 for even q and e
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c6b95a47f4ddb43102be4b2fd5d2178a
https://doi.org/10.1006/ffta.1995.1004
https://doi.org/10.1006/ffta.1995.1004
Autor:
William C. Waterhouse
Publikováno v:
Canadian Mathematical Bulletin. 37:133-139
Let F be a field containing a primitive p-th root of unity, let K / F be a cyclic extension with group 〈σ〉 of order pn, and choose a in K. This paper shows how the Galois group of the normal closure of K(a1/p) over F can be determined by computa
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::68a6584d7973c43094911af7d0776b1f
https://doi.org/10.4153/cmb-1994-019-4
https://doi.org/10.4153/cmb-1994-019-4