Symmetrical Matrices Research Articles

Introduction to Matrix Analysis

By Richard Bellman London: McGraw-Hill Publishing Co. Ltd. Pp. xx + 328. Price 77s. 6d. This volume is the first of a projected series devoted to an exposition of the results and methods of modern matrix theory, and is intended to acquaint the reader with the fundamental concepts. Starting from a consideration of maxima and minima of functions of two and more variables leads on to the consideration of quadratic forms and symmetrical matrices, the theory of which is developed in the first few chapters.

On Classification of Spherically Symmetrical Matrices (Japanese)

On Classification of Spherically Symmetrical Matrices (Japanese)

An integral which occurs in statistics

1. In this note we give a direct evaluation of the integralwhose value has been inferred from the theory of statistics. Here A = Ap = (αμν) and C = Cp = (Cμν) are real symmetrical matrices, of which A is positive definite; there are ½ p (p + 1) independent variables of integration tμν (1 ≤ μ ≤ ν ≤ p), and tμν is written also as tνμ for symmetry of notation; in the summation ∑ the variables μ, ν run independently from 1 to p; k is a real number. A word of explanation is necessary with regard to the determination of the power |A − iT|−k. Since A is positive definite and T real and symmetric, the roots of the equation