Diagonalizing matrices over C(X)

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...

Diagonalizing Operators with Reflection Symmetry

Abstract. Let U be an operator in a Hilbert space H0, and let K ⊂ H0 be a closed and invariant subspace. Suppose there is a period-2 unitary operator J in H0 such that JUJ = U, and PJP ≥ 0, where P denotes the projection of H0 onto K. We show that there is then a Hilbert space H (K), a contractive operator W : K → H (K), and a selfadjoint operator S = S (U) in H (K) such that W W = PJP , W has ...