In this paper, we study a compression of normal matrices and matrix polynomials with respect to a given vector and its orthogonal complement. The numerical range of this compression satisfies special boundary properties, which are investigated in detail. The characteristic polynomial of the compression is also considered.

We present Bayesian analyses of matrix-variate normal data with conditional independencies induced by graphical model structuring of the characterizing covariance matrix parameters. This framework of matrix normal graphical models includes prior specifications, posterior computation using Markov chain Monte Carlo methods, evaluation of graphical model uncertainty and model structure search. Ext...

In this note we will discuss the structure theorem for finitely generated modules over a principal ideal domain from the point of view of matrices. We will then give a matrixtheoretic proof of the structure theorem from the point of view of the Smith normal form of a matrix over a principal ideal domain. One benefit from this method is that there are algorithms for finding the Smith normal form...

The evolution of the degenerate complex curve associated with the ensemble at a generic critical point is related to the finite time singularities of Laplacian Growth. It is shown that the scaling behavior at a critical point of singular geometry x ∼ y is described by the first Painlevé transcendent. The regularization of the curve resulting from discretization is discussed. PACS numbers: 05.30...

Multivariate analysis of fMRI data has benefited substantially from advances in machine learning. Most recently, a range of probabilistic latent variable models applied to fMRI data have been successful in a variety of tasks, including identifying similarity patterns in neural data (Representational Similarity Analysis and its empirical Bayes variant, RSA and BRSA; Intersubject Functional Conne...

In this paper, we introduce the notions of weakly normal and normal matrix polynomials, with nonsingular leading coefficients. We characterize these matrix polynomials, using orthonormal systems of eigenvectors and normal eigenvalues. We also study the conditioning of the eigenvalue problem of a normal matrix polynomial, constructing an appropriate Jordan canonical form.

Matrix pencils, or pairs of matrices, may be used in a variety of applications. In particular, a pair of matrices (E,A) may be interpreted as the differential equation Ex′ + Ax = 0. Such an equation is invariant by changes of variables, or linear combination of the equations. This change of variables or equations is associated to a group action. The invariants corresponding to this group action...

In this note we will discuss the structure theorem for finitely generated modules over a principal ideal domain from the point of view of matrices. We will then give a matrixtheoretic proof of the structure theorem from the point of view of the Smith normal form of a matrix over a principal ideal domain. One benefit from this method is that there are algorithms for finding the Smith normal form...

The relationship between the Randic , Wiener, Hosoya , Balaban, Schultz indices, Harary numbers andDistance matrix to enthalpies of formation (Airf), heat capacity, (Cp) , enthalpies of combustion (AH °c ),enthalpy of vaporization (AH °vap) and normal boiling points (bpK)of C2 C10 normal alkanes isrepresented