David P. Kimsey

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We study the minimal normal completion problem: given A ∈ Cn×n, how do we find an (n+q)×(n+q) normal matrix Aext := ( A A12 A21 A22 ) of smallest possible size? We will show that this smallest number q of rows and columns we need to add, called the normal defect of A, satisfies nd(A) ≥ max{i−(AA∗ −A∗A), i+(AA∗ −A∗A)}, where i±(M) denotes the number of(More)
In this talk we introduce and study quaternion-valued positive definite functions on locally compact Abelian groups, real countably Hilbertian nuclear spaces and on the space of countably infinite tuples of real numbers endowed with the Tychonoff topology. In particular, we prove a quaternionic version of the Bochner-Minlos theorem. We will see that in all(More)
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