Linear and Multilinear Algebra

Multilinear forms which are products of linear forms

The conditions under which, multilinear forms (the symmetric case and the non symmetric case),can be written as a product of linear forms, are considered. Also we generalize a result due to S.Kurepa for 2n-functionals in a group G.

Numerical multilinear algebra and its applications ∗

Numerical multilinear algebra, in which instead of matrices and vectors the higher-order tensors are considered in numerical viewpoint, is a new branch of computational mathematics. Although it is an extension of numerical linear algebra, it has many essential differences from numerical linear algebra and more difficulties than it. In this paper, we present a survey on the state of the art know...

Multilinear Complexity is Equivalent to Optimal Tester Size

In this paper we first show that Tester for an F-algebra A and multilinear forms, [2], is equivalent to multilinear algorithm for the product of elements in A, [3]. Our result is constructive in deterministic polynomial time. We show that given a tester of size ν for an F-algebra A and multilinear forms of degree d one can in deterministic polynomial time construct a multilinear algorithm for t...

Dendriform Analogues of Lie and Jordan Triple Systems

We use computer algebra to determine all the multilinear polynomial identities of degree ≤ 7 satisfied by the trilinear operations (a · b) · c and a · (b · c) in the free dendriform dialgebra, where a · b is the pre-Lie or the pre-Jordan product. For the pre-Lie triple products, we obtain one identity in degree 3, and three independent identities in degree 5, and we show that every identity in ...

Notes on hadamard products of matrices - Linear and Multilinear Algebra