Congruences and canonical forms for a positive matrix: Application to the Schweinler–Wigner extremum principle
نویسندگان
چکیده
منابع مشابه
Congruences and Canonical Forms for a Positive Matrix: Application to the Schweinler-Wigner Extremum Principle
It is shown that a N ×N real symmetric [complex hermitian] positive definite matrix V is congruent to a diagonal matrix modulo a pseudo-orthogonal [pseudo-unitary] matrix in SO(m,n) [ SU(m,n)], for any choice of partition N = m+n. It is further shown that the method of proof in this context can easily be adapted to obtain a rather simple proof of Williamson’s theorem which states that if N is e...
متن کاملNearly Optimal Algorithms for Canonical Matrix Forms
A Las Vegas type probabilistic algorithm is presented for nding the Frobenius canonical form of an n n matrix T over any eld K. The algorithm requires O~(MM(n)) = MM(n) (logn) O(1) operations in K, where O(MM(n)) operations in K are suucient to multiply two n n matrices over K. This nearly matches the lower bound of (MM(n)) operations in K for this problem, and improves on the O(n 4) operations...
متن کاملthe innovation of a statistical model to estimate dependable rainfall (dr) and develop it for determination and classification of drought and wet years of iran
آب حاصل از بارش منبع تأمین نیازهای بی شمار جانداران به ویژه انسان است و هرگونه کاهش در کم و کیف آن مستقیماً حیات موجودات زنده را تحت تأثیر منفی قرار می دهد. نوسان سال به سال بارش از ویژگی های اساسی و بسیار مهم بارش های سالانه ایران محسوب می شود که آثار زیان بار آن در تمام عرصه های اقتصادی، اجتماعی و حتی سیاسی- امنیتی به نحوی منعکس می شود. چون میزان آب ناشی از بارش یکی از مولفه های اصلی برنامه ...
15 صفحه اولPositive Definite Quadratic Forms, Elliptic Curves and Cubic Congruences
Let F (x, y) = ax + bxy + cy be a positive definite binary quadratic form with discriminant Δ whose base points lie on the line x = −1/m for an integer m ≥ 2, let p be a prime number and let Fp be a finite field. Let EF : y = ax + bx + cx be an elliptic curve over Fp and let CF : ax + bx + cx ≡ 0(mod p) be the cubic congruence corresponding to F . In this work we consider some properties of pos...
متن کاملComputing codimensions and generic canonical forms for generalized matrix products
A generalized matrix product can be formally written as A sp p A sp−1 p−1 · · ·A s2 2 A s1 1 , where si ∈ {−1,+1} and (A1, . . . , Ap) is a tuple of (possibly rectangular) matrices of suitable dimensions. The periodic eigenvalue problem related to such a product represents a nontrivial extension of generalized eigenvalue and singular value problems. While the classification of generalized matri...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 1999
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.532913