EIGENVALUES AND EIGENVECTORS OF SPECTRAL DENSITY MATRICES

Abstract

This report describes some interpretations and uses of eigenvalues and eigenvectors of spectral and sample spectral density matrices of multiple stationary time series. The spectral density matrix of a zero-mean multiple stationary time series is defined. Eigenvalues and eigenvectors of the spectral density matrix are discussed and principal component theory is presented. Statistical distribution theory and related results are used to investigate the eigenvalues of a sample spectral density matrix. This investigation gives methods for obtaining simultaneous confidence bounds on the elements of the true spectral density matrix and its inverse, and also methods for obtaining confidence bounds on the eigenvalues of the true spectral density matrix.

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Document Details

Document Type
Technical Report
Publication Date
Apr 07, 1967
Accession Number
AD0814687

Entities

People

  • N. R. Goodman

Organizations

  • Teledyne Technologies

Tags

DTIC Thesaurus Topics

  • Air Force
  • Contracts
  • Data Science
  • Distribution Theory
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Estimators
  • Frequency
  • Government (Foreign)
  • Information Science
  • Probability
  • Probability Density Functions
  • Random Variables
  • Stationary
  • Statistical Distributions
  • Statistical Estimation

Fields of Study

  • Physics

Readers

  • Approximation Theory.
  • Linear Algebra