English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

For matrix convex sets a unified geometric interpretation of notions ofextreme points and of Arveson boundary points is given. These notions include,in increasing order of strength, the core notions of "Euclidean" extremepoints, "matrix" extreme points, and "absolute" extreme points. A seeminglydifferent notion, the "Arveson boundary", has by contrast a dilation theoreticflavor. An Arveson boundary point is an analog of a (not necessarilyirreducible) boundary representation for an operator system. This articleprovides and explores dilation theoretic formulations for the above notions ofextreme points.  The scalar solution set of a linear matrix inequality (LMI) is known as aspectrahedron. The matricial solution set of an LMI is a free spectrahedron.Spectrahedra (resp. free spectrahedra) lie between general convex sets (resp.matrix convex sets) and convex polyhedra (resp. free polyhedra). Asapplications of our theorems on extreme points, it is shown the polar dual of amatrix convex set K is generated, as a matrix convex set, by finitely manyArveson boundary points if and only if K is a free spectrahedron; and if thepolar dual of a free spectrahedron K is again a free spectrahedron, then at thescalar level K is a polyhedron.

Extreme points of matrix convex sets, free spectrahedra and dilation theory