Polynomial Identities For Matrices Research Articles

Polynomial identities for matrices over the Grassmann algebra

We determine minimal Cayley–Hamilton and Capelli identities for matrices over a Grassmann algebra of finite rank. For minimal standard identities, we give lower and upper bounds on the degree. These results improve on upper bounds given by L. Marki, J. Meyer, J. Szigeti and L. van Wyk in a recent paper.

*-Polynomial Identities of Matrices with the Symplectic Involution: The Low Degrees#

The *-polynomial identities of minimal degree of M n (F) are determined for n = 2, 4, * the symplectic involution.

*-polynomial identities of matrices with the transpose involution: The low degrees

In this paper, we investigate *-polynomial identities of minimal degree for the algebra of n x n matrices over a field, where n < 5 and * is the transpose involution. We first present some basic generators, and then proceed to show that all other minimal degree identities can be derived from those.

The polynomial identities of matrices in characteristic zero

The multilinear identities of the k×k matrices F2 are studied in terms of the cocharacters and codimension sequences. For F2 the estimates are fairly good, while for k≥3 only partial results are obtained.

Polynomial Identities for Matrices

(1975). Polynomial Identities for Matrices. The American Mathematical Monthly: Vol. 82, No. 4, pp. 364-368.

Polynomial Identities for Matrices

Polynomial Identities for Matrices