SOME USEFUL NOTIONS IN LINEAR VECTOR SPACES,

Abstract

Three notions regarding operators in a linear vector space are introduced: (1) the order of an element x with respect to an operator A; (2) a null-preserving operator; and (3) an orderpreserving operator. Several theorems are proved regarding these concepts, the most significant of which is theorem 8, which is the outgrowth, primarily, of the null-preserving notion. It characterizes operators of simple structure, i.e., operators whose eigenvectors span the linear vector space. Such operators constitute a larger class than the so-called normal operators whose eigenvectors are known to form an orthogonal basis in the space. The notion of an order-preserving operator is investigated very briefly, and a possible application in the investigation of the symmetric group is suggested. (Author)

Document Details

Document Type
Technical Report
Publication Date
Mar 16, 1964
Accession Number
AD0434564

Entities

People

  • N. Karayianis

Organizations

  • Harry Diamond Laboratories

Tags

DTIC Thesaurus Topics

  • Algebra
  • Eigenvectors
  • Linear Algebra
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Mathematical Modeling and Probability Theory.
  • Team-Based Human-Centered Cognitive Task Decision Making and Information Performance.

Technology Areas

  • Space