• Publications
  • Influence
Matrix analysis
This book presents results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications. Expand
Topics in Matrix Analysis
1. The field of values 2. Stable matrices and inertia 3. Singular value inequalities 4. Matrix equations and Kronecker products 5. Hadamard products 6. Functions. Expand
Matrix Analysis, 2nd Ed
A heuristic asymptotic formula concerning the distribution of prime numbers
Suppose fi, f2, -*, fk are polynomials in one variable with all coefficients integral and leading coefficients positive, their degrees being hi, h2, **. , hk respectively. Suppose each of theseExpand
The theory of infinitely divisible matrices and kernels
when he showed recently that the Green's function for Laplace's equation is, under certain conditions, an infinitely divisible kernel. In this paper we shall develop a general theory of infinitelyExpand
Estimating Heteroscedastic Variances in Linear Models
Abstract We describe an estimator of heteroscedastic variances in the Gauss-Markov linear model where E(e) = 0 and with σ i 2 and unknown. It may be thought of as an approximation to the MINQUEExpand
A generalization of the complex Autonne–Takagi factorization to quaternion matrices
A complex symmetric matrix A can always be factored as A = UΣU T , in which U is complex unitary and Σ is a real diagonal matrix whose diagonal entries are the singular values of A. ThisExpand
Canonical matrices of bilinear and sesquilinear forms
Abstract Canonical matrices are given for (i) bilinear forms over an algebraically closed or real closed field; (ii) sesquilinear forms over an algebraically closed field and over real quaternionsExpand
Block-matrix generalizations of Schur's basic theorems on Hadamard products
Abstract In a classic 1911 paper, I. Schur gave several useful bounds for the spectral norm and eigenvalues of the Hadamard (entrywise) product of two matrices. Motivated by applications to theExpand