کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4599252 1631126 2015 30 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Change of the congruence canonical form of 2-by-2 and 3-by-3 matrices under perturbations and bundles of matrices under congruence
ترجمه فارسی عنوان
تغییر شکل کانونی همگرایی ماتریس های 2 تا 2 و 3 به 3 تحت اختلالات و دسته های ماتریس ها تحت همبستگی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

We construct the Hasse diagrams G2G2 and G3G3 for the closure ordering on the sets of congruence classes of 2×22×2 and 3×33×3 complex matrices. In other words, we construct two directed graphs whose vertices are 2×22×2 or, respectively, 3×33×3 canonical matrices under congruence, and there is a directed path from A to B if and only if A can be transformed by an arbitrarily small perturbation to a matrix that is congruent to B.A bundle of matrices under congruence is defined as a set of square matrices A   for which the pencils A+λATA+λAT belong to the same bundle under strict equivalence. In support of this definition, we show that all matrices in a congruence bundle of 2×22×2 or 3×33×3 matrices have the same properties with respect to perturbations. We construct the Hasse diagrams G2B and G3B for the closure ordering on the sets of congruence bundles of 2×22×2 and, respectively, 3×33×3 matrices. We find the isometry groups of 2×22×2 and 3×33×3 congruence canonical matrices.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 469, 15 March 2015, Pages 305–334
نویسندگان
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