Polynomial Identities for Hypermatrices
نویسنده
چکیده
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.
منابع مشابه
Rings with a setwise polynomial-like condition
Let $R$ be an infinite ring. Here we prove that if $0_R$ belongs to ${x_1x_2cdots x_n ;|; x_1,x_2,dots,x_nin X}$ for every infinite subset $X$ of $R$, then $R$ satisfies the polynomial identity $x^n=0$. Also we prove that if $0_R$ belongs to ${x_1x_2cdots x_n-x_{n+1} ;|; x_1,x_2,dots,x_n,x_{n+1}in X}$ for every infinite subset $X$ of $R$, then $x^n=x$ for all $xin R$.
متن کاملar X iv : m at h - ph / 0 20 80 10 v 2 7 A ug 2 00 2 ALGEBRAIC INVARIANTS , DETERMINANTS , AND CAYLEY – HAMILTON THEOREM FOR HYPERMATRICES . THE FOURTH – RANK CASE
We develop a method to construct algebraic invariants for hypermatrices. We then construct hyperdeterminants and exhibit a generalization of the Cayley–Hamilton theorem for hypermatrices.
متن کاملar X iv : m at h - ph / 0 20 80 10 v 1 6 A ug 2 00 2 ALGEBRAIC INVARIANTS , DETERMINANTS , AND CAYLEY – HAMILTON THEOREM FOR HYPERMATRICES . THE FOURTH – RANK CASE
We develop a method to construct algebraic invariants for hypermatrices. We then construct hyperdeterminants and exhibit a generalization of the Cayley–Hamilton theorem for hypermatrices.
متن کاملSupersymmetric Hypermatrix Lie Algebra and Hypermatrix Groups Generated by the Dihedral Set D3
This work is an investigation into the structure and properties of supersymmetric hypermatrix Lie algebra generated by elements of the dihedral group D3. It is based on previous work on the subject of supersymmetric Lie algebra (Schreiber, 2012). In preview work I used several new algebraic tools; namely cubic hypermatrices (including special arrangements of such hypermatrices) and I obtained a...
متن کاملSpectra of Uniform Hypergraphs
We present a spectral theory of uniform hypergraphs that closely parallels Spectral Graph Theory. A number of recent developments building upon classical work has led to a rich understanding of “symmetric hyperdeterminants” of hypermatrices, a.k.a. multidimensional arrays. Symmetric hyperdeterminants share many properties with determinants, but the context of multilinear algebra is substantiall...
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 2008