Universal Identities , Ii : ⊗ and ∧
نویسنده
چکیده
Theorem 1.1. Let R be a commutative ring and n be a positive integer. For any A ∈ Mn(R), write its characteristic polynomial as det(TIn −A) = T + c1(A)T + · · ·+ cn−1(A)T + cn(A) ∈ R[T ]. Then ck(A) = (−1)k Tr(∧k(A)). Note the indexing: the coefficient of Tn−k is associated to the kth exterior power of A. In the special cases k = 1 and k = n this recovers the more familiar result that c1(A) = −Tr(A) and cn(A) = (−1)n det(A). Here are two more theorems about multilinear operations on matrices.
منابع مشابه
تأثیر ادهزیوهای توتال اچ و یونیورسال بر روی ریز نشت بین کامپوزیت و گلاس آینومر در ترمیمهای ساندویچ کلاس II
Background and purpose: Microleakage is the most common cause of secondary caries and failure of restorations. The aim of this study was to evaluate the Microleakage between resin modified glass-ionomer (RMGI) and resin composite in sandwich restorations using different bonding agents. Materials and methods: Forty four premolars were used in this experimental study. Class II cavities were prep...
متن کاملMore on Five Commutator Identities
We prove that five well-known identities universally satisfied by commutators in a group generate all universal commutator identities for commutators of weight 4.
متن کاملUniversality of one-dimensional Fermi systems, II. The Luttinger liquid structure
We complete the proof started in [1] of the universal Luttinger liquid relations for a general model of spinning fermions on a lattice, by making use of the Ward Identities due to asymptotically emerging symmetries. This is done by introducing an effective model verifying extra symmetries and by relating its critical exponents to those of the fermion lattice gas by suitable fine tuning of the p...
متن کاملThe Comparison of Shear Bond Strength of Self-cured and Light-cured Composite Restorations to Dentin, Using a Universal Bonding System
Introduction: To evaluate and compare shear bond strength of self-cure and light-cure composites using a universal bonding system. Materials and Methods: Superficial coronal dentin of 62 intact extracted premolars was exposed and bonding agent (All-Bond Universal) was applied over the dentin surface according to the manufacturer instruction (self-etch mode). Then samples were distribut...
متن کاملComparative Evaluation of microleakage of Bulk-fill and Posterior Composite Resins Using the Incremental Technique and a Liner in Cl II Restorations
Background and Aim: In recent years there has been a surge in the use of tooth-colored restorations. However, the polymerization shrinkage of these materials can form gaps, resulting in microleakage. This study aimed to compare microleakage by using different materials and techniques. Materials and Methods: In this experimental study, Cl II cavities were prepared on the mesial surfaces of 60 s...
متن کاملContemporary Iranian Dramatist, Eastern Visual Provocation, and Cultural Originality
The necessity of taking refuge in literary productions has been intensified due to the societies’ severe involvement in the features of the modern world. Loss of identity and failure to maintain an integrated self are the repercussions of distancing from humanistic roots. Some attempts in modern art/literature appear to focus more on visual styles to represent the catastrophes of the modern uni...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014