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Compressions of Totally Positive Matrices
SIAM Journal on Matrix Analysis and Applications, 2006The 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.
Allen Herman, Shaun M Fallat
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Almost strictly totally positive matrices
Numerical Algorithms, 1992zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Juan Manuel Pena +2 more
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On the Relationship Between Graphs and Totally Positive Matrices
SIAM Journal on Matrix Analysis and Applications, 1998A 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.
Juan Manuel Pena
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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
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A Totally Positive Factorization of Rectangular Matrices by the Neville Elimination
SIAM Journal on Matrix Analysis and Applications, 2004The 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
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