Let Mn(F) be the algebra of n×n matrices over a field F, and let A∈Mn(F) have characteristic polynomial c(x)=p1(x)p2(x)⋯pr(x) where p1(x),…,pr(x) are distinct and irreducible in F[x]. Let X be a subalgebra of Mn(F) containing A. Under a mild hypothesis on the pi(x), we find a necessary and sufficient condition for X to be Mn(F).
關聯:
Linear Algebra and Its Applications 37, pp.199-204
