A Note on Nilpotent Lattice Matrices

نویسندگان

  • A. Moussavi
  • Ali Ahmadi
چکیده

Some properties and characterizations for nilpotent matrices are established and in particular, a necessary and sufficient condition for an n × n nilpotent matrix to have the nilpotent index 2 and 3 is given. Mathematics Subject Classification: 15A33; 06D99

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Residuated Skew Lattice with a Operation

In this paper, we define hedge operation on a residuated skew lattice and investigate some its properties. We get relationships between some special sets as dense, nilpotent, idempotent, regular elements sets and their hedges.  By examples, we show that hedge of a dense element is not a dense and hedge of a regular element is not a regular. Also hedge of a nilpotent element is a nilpotent and h...

متن کامل

On the nil-clean matrix over a UFD

 In this paper we characterize all $2times 2$ idempotent and nilpotent matrices over an integral domain and then we characterize all $2times 2$ strongly nil-clean matrices over a PID. Also, we determine when a $2times 2$ matrix  over a UFD is nil-clean.

متن کامل

A Note on Decomposing a Square Matrix as Sum of Two Square Nilpotent Matrices over an Arbitrary Field

Let K be an arbitrary field and X a square matrix over K. Then X is sum of two square nilpotent matrices over K if and only if, for every algebraic extension L of K and arbitrary nonzero α ∈ L, there exist idempotent matrices P 1 and P 2 over L such that X = αP 1 - αP 2.

متن کامل

COMPUTATIONAL ENUMERATION OF POINT DEFECT CLUSTERS IN DOUBLE- LATTICE CRYSTALS

The cluster representation matrices have already been successfully used to enumerate close-packed vacancy clusters in all single-lattice crystals [I, 2]. Point defect clusters in double-lattice crystals may have identical geometry but are distinct due to unique atomic postions enclosing them. The method of representation matrices is extended to make it applicable to represent and enumerate ...

متن کامل

2 00 5 Notes on ( twisted ) lattice supersymmetry

We describe a new approach to the problem of putting supersymmetric theories on the lattice. The basic idea is to discretize a twisted formulation of the supersymmetric theory. For certain theories with extended supersymmetry these twisted formulations contain only integer spin fields. The twisting exposes a scalar nilpotent supercharge which generates an exact lattice symmetry. We gives exampl...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2010