Skip to main content
Open Access Publications from the University of California

UC Berkeley

UC Berkeley Previously Published Works bannerUC Berkeley

Can one factor the classical adjoint of a generic matrix?

  • Author(s): Bergman, George M
  • et al.

Let k be an integral domain, n a positive integer, X a generic n x n matrix over k (i.e., the matrix (xij) over a polynomial ring k[xij] in n2 indeterminates xij): and adj(X) its classical adjoint. For char k = 0, it is shown that if n is odd, adj(X) is not the product of two noninvertible n x n matrices over k[xij], while for n even, only one special sort of factorization occurs. Whether the corresponding results hold in positive characteristic is not known. The operation adj on matrices arises from the (n-1)st exterior power functor on modules; the analogous factorization question for matrix constructions arising from other functors is raised, as are several other questions.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
For improved accessibility of PDF content, download the file to your device.
Current View