Trace identities and polynomial identities of n × n matrices
نویسندگان
چکیده
منابع مشابه
ON SUBALGEBRAS OF n× n MATRICES NOT SATISFYING IDENTITIES OF DEGREE 2n− 2
The Amitsur-Levitzki theorem asserts that Mn(F ) satisfies a polynomial identity of degree 2n. (Here, F is a field and Mn(F ) is the algebra of n × n matrices over F ). It is easy to give examples of subalgebras of Mn(F ) that do satisfy an identity of lower degree and subalgebras of Mn(F ) that satisfy no polynomial identity of degree ≤ 2n − 2. In this paper we prove that the subalgebras of n ...
متن کاملInvariants and polynomial identities for higher rank matrices
We exhibit explicit expressions, in terms of components, of discriminants, determinants, characteristic polynomials and polynomial identities for matrices of higher rank. We define permutation tensors and in term of them we construct discriminants and the determinant as the discriminant of order d, where d is the dimension of the matrix. The characteristic polynomials and the Cayley–Hamilton th...
متن کاملPolynomial identities for partitions
For any partition λ of an integer n , we write λ =< 11, 22, . . . , nn > where mi(λ) is the number of parts equal to i . We denote by r(λ) the number of parts of λ (i.e. r(λ) = ∑n i=1mi(λ) ). Recall that the notation λ ` n means that λ is a partition of n . For 1 ≤ k ≤ N , let ek be the k-th elementary symmetric function in the variables x1, . . . , xN , let hk be the sum of all monomials of to...
متن کاملInterprocedurally Analyzing Polynomial Identities
Since programming languages are Turing complete, it is impossible to decide for all programs whether a given non-trivial semantic property is valid or not. The way-out chosen by abstract interpretation is to provide approximate methods which may fail to certify a program property on some programs. Precision of the analysis can be measured by providing classes of programs for which the analysis ...
متن کاملPolynomial Identities for Hypermatrices
We develop an algorithm to construct algebraic invariants for hypermatrices. We then construct hyperdeterminants and exhibit a generalization of the Cayley–Hamilton theorem for hypermatrices.
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 Algebra
سال: 1976
ISSN: 0021-8693
DOI: 10.1016/0021-8693(76)90104-6