Counterexamples concerning the diagonal elements of normal matrices

On Constructing Matrices with Prescribed Singular Values and Diagonal Elements

Similar to the well known Schur Horn theorem that characterizes the relationship between the diagonal entries and the eigenvalues of a Hermitian matrix the Sing Thompson theorem characterizes the relationship between the diagonal en tries and the singular values of an arbitrary matrix It is noted in this paper that based on the induction principle such a matrix can be constructed numerically by...

Concerning Matrices with Elements in a Commutative Ring*

Counterexamples concerning a Weighted L2 Projection

Counterexamples are given to show that some results concerning a weighted L projection presented earlier by Bramble and the author are sharp, i.e., that certain error and stability estimates are impossible in some cases.

Counterexamples to three conjectures concerning perfect graphs

We will present counterexamples to a conjecture of Hoàng, a conjecture of Hertz and de Werra and to a conjecture of Reed. All these three conjectures are related to perfect graphs.

Tests Concerning Equicorrelation Matrices with Grouped Normal Data

This paper considers three practical hypotheses involving the equicorrelation matrix for grouped normal data. We obtain statistics and computing formulae for common test procedures such as the score test and the likelihood ratio test. In addition, statistics and computing formulae are obtained for various small sample procedures as proposed in Skovgaard (2001). The properties of the tests for e...