We consider a certain decomposition of the matrix algebra Mn (F), where F is a field. The commutation relations of that decomposition yield an n2 × n2 matrix MMn (F), which determines the multilinear polynomial identities of Mn (F). Thus if char (F) = 0, the matrix MMn (F) determines the polynomial identities of Mn (F). We show that MMn (F) is very close to the tensor product of two n × n Vandermonde matrices. In particular this allows us to evaluate the determinant of MMn (F).
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics