I. Bundles of Matrices and the Linear Independence of Their Minors: II. Applications of Laguerre's Method to the Matrix Eigenvalue Problem
DE CRIPTOR : (*Radio signal , Reflection, M OO * G O-OP IC ROTATION, ASUR ENT ) (Ionospheric propagation, Radio transmission, *Wave tran is ion, Polarization, Correlation techniques.) Radio astronomy.A method of measuring the Faraday rotation of the plane of polarization of a radio wave on a rip to and from the moon is briefly described. Equatio s are pr s ed which m y be u ed to calculate the to al electron content in the ionosphere, using he Faraday fading period and t differe ce bet en th pol ri ion angles fre u nci . Criteria re given for selecting the second frequency. The methods of analyzing the data to determine the Faraday fading perio and polarization difference are described. A method of correlation analysis is presented. Equations are given for calculating the autocorrelation, cross-corr lation, nd spectra from experimental data. The methods of data analysis are applied to data taken on 31 July 1960. (Author).
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k A WellKhown Lemma
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abs ybar ABS(YBAR absmax accuracy ALGOL ALPHA approximation arbitrary bundles basis vector booil bundles are strictly Burroughs 220 calculate canonical form characteristic polynomial coefficients complex convergence Correct Computed Criterion denote derivatives determinant determinantal ideals double precision eigenvalue problem eigenvectors eigsum2 elementary divisors equation evaluation EXTERNAL PROCEDURE greatest common divisors Hessenberg form Hessenberg matrix Hy end Hyman's method imaginary initial vector inner product IROOT Laguerre iterates Laguerre's method lanczos Lemma linearly independent subset linearly independent t-minors m x n maximal linearly independent n x n matrix Newton iterate non-singular non-zero Note null number of iterations obtain OUTPUT pencils polynomials of degree precision number principal ideal ring Proof real roots regular bundles row j+l Section set of determinantal single precision spur spur2 spurl step strictly equivalent subtract superdiagonal Symmetric Matrix tally Theorem tridiagonal form tridiagonal matrix xbar zero