A note on symetric matrices
A note on symplectic block reflectors.
A note on the complex and real operator norms of real matrices
A note on the continuity of projection matrices with application to the asymptotic distribution of quadratic forms
This paper investigates the continuity of projection matrices and illustrates an important application of this property to the derivation of the asymptotic distribution of quadratic forms. We give a new proof and an extension of a result of Stewart (1977).
A note on the convexity of the realizable set of eigenvalues for nonnegative symmetric matrices.
A note on the cp-rank of matrices generated by Soules matrices.
A note on the determinant of a Toeplitz-Hessenberg matrix
The nth-order determinant of a Toeplitz-Hessenberg matrix is expressed as a sum over the integer partitions of n. Many combinatorial identities involving integer partitions and multinomial coefficients can be generated using this formula.
A note on the general Hermitian solution to .
A note on the Hankel transform of the central binomial coefficients.
A note on the integral criterion for spectral dichotomy of regular pencils.
A note on the inversion of Sylvester matrices in control systems.
A note on the iteration of infinite matrices
A note on the largest eigenvalue of non-regular graphs.
A note on the matrix Haffian.
This note contains a transparent presentation of the matrix Haffian. A basic theorem links this matrix and the differential ofthe matrix function under investigation, viz ∇F(X) and dF(X).Frequent use is being made of matrix derivatives as developed by Magnus and Neudecker.
A Note on the Permanental Roots of Bipartite Graphs
It is well-known that any graph has all real eigenvalues and a graph is bipartite if and only if its spectrum is symmetric with respect to the origin. We are interested in finding whether the permanental roots of a bipartite graph G have symmetric property as the spectrum of G. In this note, we show that the permanental roots of bipartite graphs are symmetric with respect to the real and imaginary axes. Furthermore, we prove that any graph has no negative real permanental root, and any graph containing...
A note on the ranks of set-inclusion matrices.
A note on the reverse order laws for - and -inverses of multiple matrix products.
A note on the scalar Haffian.
In this note a uniform transparent presentation of the scalar Haffian will be given. Some well-known results will be generalized. A link will be established between the scalar Haffian and the derivative matrix as developed by Magnus and Neudecker.
A note on the spectra of tridiagonal matrices.
A Note on the Structure of the Semigroup of Doubly-Stochastic Matrices