Matricial inner products and pointed cones of hermitian-preserving linear transformations

✍ Scribed by Joseph R. Siler; Richard D. Hill

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 360 KB
• Volume: 257
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(96)00205-4

✦ Synopsis

Let ~ be a conjugate-homogeneous reflector on a vector space V (over R or C) with ~.~ a pointed cone contained in spec,~(V). A mapping on V X V whose range is contained in ~ which generalizes the usual inner product properties is called a vectorial inner product. A certain family of these vectorial inner products on matrices (which we call matricial inner products) is used to generate a set of pointed cones in the ambient space of hermitian-preserving linear transformations. Some basic results on these cones [including ~'(PSD), ~r(PSD)*, and ~'.~] and on the partial orders that they induce are given.