A Note on Positive Semi-Definiteness of Some Non-Pearsonian Correlation Matrices

A note on positive deniteness and stability of interval matrices

It is proved that by using bounds of eigenvalues of an interval matrix, someconditions for checking positive deniteness and stability of interval matricescan be presented. These conditions have been proved previously with variousmethods and now we provide some new proofs for them with a unity method.Furthermore we introduce a new necessary and sucient condition for checkingstability of interval...

A note on positive deniteness and stability of interval matrices

It is proved that by using bounds of eigenvalues of an interval matrix, someconditions for checking positive deniteness and stability of interval matricescan be presented. These conditions have been proved previously with variousmethods and now we provide some new proofs for them with a unity method.Furthermore we introduce a new necessary and sucient condition for checkingstability of interval...

Positive definiteness of tridiagonal matrices via the numerical range

Positive Semi-definiteness of Generalized Anti-circulant Tensors

Anti-circulant tensors have applications in exponential data fitting. They are special Hankel tensors. In this paper, we extend the definition of anti-circulant tensors to generalized anticirculant tensors by introducing a circulant index r such that the entries of the generating vector of a Hankel tensor are circulant with module r. In the special case when r=n, where n is the dimension of the...

A note on “ 5 × 5 Completely positive matrices ”

In their paper “5×5 Completely positive matrices,” Berman and Xu [BX04] attempt to characterize which 5× 5 doubly nonnegative matrices are also completely positive. Most of the analysis in [BX04] concerns a doubly nonnegative matrix A that has at least one off-diagonal zero component. To handle the case where A is componentwise strictly positive, Berman and Xu utilize an “edge-deletion” transfo...