zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On the cone of completely positive linear transformations. (English) Zbl 0959.15026
Authors’ abstract: All faces (and specifically extremals) of the cone $\text{CP}_{m,n}$ are characterized as are its interior and boundary.

MSC:
15B48Positive matrices and their generalizations; cones of matrices
15A04Linear transformations, semilinear transformations (linear algebra)
WorldCat.org
Full Text: DOI
References:
[1] Barker, G. P.: Faces and duality in convex cones. Linear and multilinear algebra 6, 161-169 (1978)
[2] Barker, G. P.: Theory of cones. Linear algebra appl. 39, 263-291 (1981) · Zbl 0467.15002
[3] Barker, G. P.; Carlson, D.: Cones of diagonally dominant matrices. Pacific J. Math. 57, 15-32 (1975) · Zbl 0283.52005
[4] Barker, G. P.; Hill, R. D.; Haertel, R. D.: On the completely positive and positive-semidefinite-preserving cones. Linear algebra appl. 56, 221-229 (1984) · Zbl 0534.15012
[5] Barker, G. P.; Schneider, H.: Algebraic Perron--Frobenius theory. Linear algebra appl. 11, 219-233 (1975) · Zbl 0311.15011
[6] G. Birkhoff, Lattice Theory, third ed., American Mathemtical Society, Providence. RI, 1967 · Zbl 0153.02501
[7] Choi, M.: Completely positive linear maps on complex matrices. Linear algebra appl. 10, 285-290 (1975) · Zbl 0327.15018
[8] Hill, R. D.: Inertia theory for simultaneously triangulable complex matrices. Linear algebra appl. 2, 131-142 (1969) · Zbl 0186.33901
[9] Hill, R. D.; Waters, S. R.: On the cone of positive semidefinite matrices. Linear algebra appl. 90, 81-88 (1987) · Zbl 0615.15008
[10] Loewy, R.; Schneider, H.: Indecomposable cones. Linear algebra appl. 11, 235-245 (1975) · Zbl 0316.47026
[11] P. Lancaster, M. Tismenetsky, The Theory of Matrices, Academic press, New York, 1985 · Zbl 0558.15001
[12] Oxenrider, C. J.; Hill, R. D.: On the matrix reorderings ${\Gamma}$ and ${\Psi}$. Linear algebra appl. 69, 205-212 (1985) · Zbl 0573.15001
[13] Poluikis, J. A.; Hill, R. D.: Completely positive and Hermitian-preserving linear transformations. Linear algebra appl. 35, 1-10 (1981) · Zbl 0451.15013
[14] Schneider, H.; Vidyasagar, M.: Cross-positive matrices. SIAM J. Numer. anal. 7, 508-519 (1970) · Zbl 0245.15008
[15] Tam, B. S.: On the semiring of cone preserving maps. Linear algebra appl. 35, 79-108 (1981) · Zbl 0454.16025
[16] Tam, B. S.: On the structure of the cone of positive operators. Linear algebra appl. 167, 65-85 (1992) · Zbl 0755.15010
[17] D.A. Yopp, Cone Preserving linear transformations, D.A. Thesis, Idaho State University, Pocatello, Id., 1998
[18] D.A. Yopp, R.D. Hill, Extreme rays of the cone of linear transformations that preserve the positive semidefinite matrices, In progress