40 citations · 250 across the 28 of their papers we have counts for
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The joint numerical range of three hermitian matrices
Piotr Pikul, Ilya Spitkovsky, Konrad Szymański +2
We analyze the joint numerical range of three hermitian matrices of order four. In the generic case, this three-dimensional convex set has a smooth boundary. We analyze non-gen…
Matrix systems, algebras, and open maps
Stephan Weis
Every state on the algebra of complex nxn matrices restricts to a state on any matrix system. Whereas the restriction to a matrix system is generally not open, we prove that…
Kippenhahn's construction revisited
Stephan Weis
Kippenhahn discovered that the numerical range of a complex square matrix is the convex hull of a plane real algebraic curve. Here, we present an example of a convex set, which has…
The face generated by a point, generalized affine constraints, and quantum theory
Stephan Weis, Maksim Shirokov
We analyze faces generated by points in an arbitrary convex set and their relative algebraic interiors, which are nonempty as we shall prove. We show that by intersecting a convex…
Classification of joint numerical ranges of three hermitian matrices of size three
Konrad Szymański, Stephan Weis, Karol Życzkowski
The joint numerical range of three hermitian -by- matrices is a convex and compact subset in . Generically we find that is a thr…
Pre-images of extreme points of the numerical range, and applications
Ilya M. Spitkovsky, Stephan Weis
We extend the pre-image representation of exposed points of the numerical range of a matrix to all extreme points. With that we characterize extreme points which are multiply gener…