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Advances on strictly Δ -modular IPs. [PDF]

Math Program
Nägele M, Nöbel C, Santiago R, Zenklusen R.   +3 more
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Compressions of Totally Positive Matrices

SIAM Journal on Matrix Analysis and Applications, 2006
The paper deals with the total positivity of the compressed matrix of a totally positive matrix \(A\). Consider \(nk \times nk\) partitioned matrices \(A=(A_{ij})_{i,j=1}^k\), in which each block \(A_{ij}\) is \(n \times n\). The \(k \times k\) compressed matrix is defined by \[ C_k(A)=(\det A_{ij})_{i,j=1}^k.
Shaun M Fallat, Allen Herman
exaly   +3 more sources

Almost strictly totally positive matrices

Numerical Algorithms, 1992
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
M Gasca, Charles A Micchelli, J M Pena
exaly   +2 more sources

On the Relationship Between Graphs and Totally Positive Matrices

SIAM Journal on Matrix Analysis and Applications, 1998
A real matrix is totally positive if all its minors are non-negative. It is shown that properties of totally positive matrices can be applied to graph theory and vice versa. In fact, some properties of undirected and directed graphs are characterized in terms of the associated totally positive matrices.
J M Pena
exaly   +3 more sources

Totally Positive Matrices

, 2009
Totally positive matrices constitute a particular class of matrices, the study of which was initiated by analysts because of its many applications in diverse areas. This account of the subject is comprehensive and thorough, with careful treatment of the central properties of totally positive matrices, full proofs and a complete bibliography.
Pinkus, Allan
openaire   +2 more sources

A Totally Positive Factorization of Rectangular Matrices by the Neville Elimination

SIAM Journal on Matrix Analysis and Applications, 2004
The authors describe a variant of the Neville elimination process for a real matrix with all non-negative minors. Such a matrix is called a totally positive \((TP)\) matrix. The proposed method is called quasi-Neville method, it allows, for every rectangular \(TP\) matrix \(A\), a factorization \(A=LS\), where \(L\) is a lower echelon form matrix and \(
Juan R Torregrosa
exaly   +2 more sources

A new look at totally positive matrices [PDF]

Czechoslovak Mathematical Journal, 2016
summary:A close relationship between the class of totally positive matrices and anti-Monge matrices is used for suggesting a new direction for investigating totally positive matrices.
Miroslav Fiedler
exaly   +3 more sources

Hadamard powers and totally positive matrices

Linear Algebra and Its Applications, 2007
Considered are continuous, positive Hadamard powers of entry-wise positive (nonnegative) matrices. Those that are eventually (in the sense of all Hadamard powers beyond some point) totally positive, totally nonnegative, doubly nonnegative and doubly ...
Shaun M Fallat
exaly   +2 more sources