Ela Tpk Completion of Partial Matrices with One Unspecified Entry
نویسنده
چکیده
Abstract. Every partial TP2 (TP1) matrix with one unspecified entry has a TP2 (TP1) completion. For a given m-by-n pattern with one unspecified entry, the minimum set of conditions characterizing TP3 completability is given. These conditions are at most eight polynomial inequalities on the specified entries of the pattern. For k ≥ 3, patterns with one unspecified entry that are TPk completable are also characterized, and conditions are described for completability otherwise.
منابع مشابه
The General Totally Positive Matrix Completion Problem with Few Unspecified Entries
For m by n partial totally positive matrices with exactly one unspeci ed entry the set of positions for that entry that guarantee completability to a totally positive matrix are characterized They are the positions i j i j and the positions i j i j m n In each case the set of completing entries is an open and in nite in case i j or i m j n interval In the process some new structural results abo...
متن کاملPOSITIVE DEFINITE COMPLETION PROBLEMS FOR DIRECTED ACYCLIC GRAPHS By
A positive definite completion problem pertains to determining whether the unspecified positions of a partial (or incomplete) matrix can be completed in a desired subclass of positive definite matrices. In this paper we study an important and new class of positive definite completion problems where the desired subclasses are the spaces of covariance and inverse-covariance matrices of probabilis...
متن کاملSingular, Nonsingular, and Bounded Rank Completions of ACI-Matrices
An affine column independent matrix is a matrix whose entries are polynomials of degree at most 1 in a number of indeterminates where no indeterminate appears with a nonzero coefficient in two different columns. A completion is a matrix obtained by giving values to each of the indeterminates. Affine column independent matrices are more general than partial matrices where each entry is either a ...
متن کاملEla Generalized Schur Complements of Matrices and Compound Matrices
In this paper, we obtain some formulas for compound matrices of generalized Schur complements of matrices. Further, we give some Löwner partial orders for compound matrices of Schur complements of positive semidefinite Hermitian matrices, and obtain some estimates for eigenvalues of Schur complements of sums of positive semidefinite Hermitian matrices.
متن کاملThiamine pyrophosphate biosynthesis and transport in the nematode Caenorhabditis elegans.
Thiamine (vitamin B1) is required in the diet of animals, and thiamine deficiency leads to diseases such as beri-beri and the Wernicke-Korsakoff syndrome. Dietary thiamine (vitamin B1) consists mainly of thiamine pyrophosphate (TPP), which is transformed into thiamine by gastrointestinal phosphatases before absorption. It is believed that TPP itself cannot be transported across plasma membranes...
متن کامل