In this paper, we first consider the existence of and the general expression for the solution to the constrained inverse eigenproblem defined as follows: given a set of complex n-vectors {xi}i=1 and a set of complex numbers {λi}i=1, and an s-by-s real matrix C0, find an n-by-n real centrosymmetric matrix C such that the s-by-s leading principal submatrix of C is C0, and {xi}i=1 and {λi}i=1 are ...

A matrix always has a full rank submatrix such that the of this is equal to submatrix. This property one corner stones theory. We call max-full-rank-submatrix property. Tensor ranks play crucial role in low tensor approximation, completion and recovery. However, their theory still not matured yet. Can we set an axiom system for ranks? extend tensors? explore these paper. first propose some axio...

For integer n>0, let f(n) be the number of rows largest all-0 or all-1 square submatrix M, minimized over all n×n 0/1-matrices M. Thus f(n)=O(log⁡n). But us fix a matrix H, and define fH(n) to same, M such that neither nor its complement (that is, change 0's 1's vice versa) contains H as submatrix. It is known fH(n)≥εnc, where c,ε>0 are constants depending on H. When can we take c=1? If so, the...

We investigate the computational complexity of some basic problems regarding non-unique probe selection using separable matrices. In particular, we prove that the Minimal d̄-Separable Matrix problem is DP -complete, and the d̄-Separable Submatrix with Reserved Rows problem, which is a generalization of the decision version of the Minimum d̄-Separable Submatrix problem, is Σ2 -complete.

We develop an algorithmically useful refinement of a forbidden submatrix characterization of 0/1-matrices fulfilling the Consecutive Ones Property (C1P). This characterization finds applications in new polynomial-time approximation algorithms and fixed-parameter tractability results for the NP-hard problem to delete a minimum number of rows or columns from a 0/1-matrix such that the remaining s...