Journal ArticleDOI
Inheritance and inverse monotonicity properties of copositive matrices
Kavita Bisht,K. C. Sivakumar +1 more
TLDR
In this article, the inheritance property of the Schur complement of a copositive matrix is extended to the case when the inverses in Schur complements are replaced by their Moore-Penrose inverse.Abstract:
A symmetric matrix is called copositive if it satisfies the inequality whenever and strictly copositive if , whenever . The ordering of a vector here is component-wise. Certain interesting properties of the inverse of a copositive matrix are extended to its Moore–Penrose inverse. The inheritance property of the Schur complement of a copositive matrix is extended to the case when the inverses in the Schur complement are replaced by their Moore–Penrose inverses. A framework is provided wherein one has the copositivity of , given the copositivity of .read more
References
More filters
Book
Generalized inverses: theory and applications
Adi Ben-Israel,T. N. E. Greville +1 more
TL;DR: In this paper, the Moore of the Moore-Penrose Inverse is described as a generalized inverse of a linear operator between Hilbert spaces, and a spectral theory for rectangular matrices is proposed.
BookDOI
The Schur complement and its applications
TL;DR: Schur complements in statistics and probability have been used in Numerical Analysis as mentioned in this paper, where the Schur Complement has been applied in statistical and probability analysis. But their application is limited to statistical analysis.
Journal ArticleDOI
A Variational Approach to Copositive Matrices
TL;DR: This work surveys essential properties of the so-called copositive matrices, the study of which has been spread over more than fifty-five years, with special emphasis on variational aspects related to the concept of copositivity.
Journal ArticleDOI
Criteria for copositive matrices
TL;DR: In this article, finite criteria for copositive matrices are proposed and compared with existing determinantal tests, including principal pivoting and principal pivot-based matrices, and the basic mathematical tool is principal pivot.
Journal ArticleDOI
Spectral theory of copositive matrices
Charles R. Johnson,Robert Reams +1 more
TL;DR: In this paper, a block characterization of copositive matrices with the assumption that one of the principal blocks is positive definite is given, and it is shown that for any matrix A ∈ R n × n, if A has a positive vector in the subspace spanned by the eigenvectors corresponding to its nonnegative eigenvalues, then it is possible to increase the nonnegative values of A without changing the matrix's eigenvector.