Diagonalizing matrices over operator algebras

Diagonalizing Matrices over Aw*-algebras

Every commuting set of normal matrices with entries in an AW*algebra can be simultaneously diagonalized. To establish this, a dimension theory for properly infinite projections in AW*-algebras is developed. As a consequence, passing to matrix rings is a functor on the category of AW*-

Approximately diagonalizing matrices over C(Y).

Let X be a compact metric space which is locally absolutely retract and let ϕ: C(X) → C(Y,M(n)) be a unital homomorphism, where Y is a compact metric space with dim Y ≤ 2. It is proved that there exists a sequence of n continuous maps α(i,m): Y → X (i = 1,2,…,n) and a sequence of sets of mutually orthogonal rank-one projections {p(1,m),p(2,m),…,p(n,m)} C(Y,M(n)) such that [see formula]. This is...

Diagonalizing Matrices

On Tridiagonalizing and Diagonalizing Symmetric Matrices with Repeated Eigenvalues

We describe a divide-and-conquer tridiagonalizationapproach for matrices with repeated eigenvalues. Our algorithmhinges on the fact that, under easily constructivelyveriiable conditions,a symmetricmatrix with bandwidth b and k distinct eigenvalues must be block diagonal with diagonal blocks of size at most bk. A slight modiication of the usual orthogonal band-reduction algorithm allows us to re...

Poincaré Supersymmetry Representations Over Trace Class Noncommutative Graded Operator Algebras

We show that rigid supersymmetry theories in four dimensions can be extended to give supersymmetric trace (or generalized quantum) dynamics theories, in which the supersymmetry algebra is represented by the generalized Poisson bracket of trace supercharges, constructed from fields that form a trace class noncommutative graded operator algebra. In particular, supersymmetry theories can be turned...