The Inverse of a Boolean Matrix

Abstract

The paper describes the necessary and sufficient conditions for a Boolean matrix to have a left and a right inverse. Boolean matrices are arrays of Boolean functions just as ordinary matrices are arrays of numbers. The rules for Boolean matrix multiplication are the same as for ordinary matrix multiplication, except that summation is replaced by logical summation, and the product is replaced by a logical product. Note that the elements of the matrices might just be 0 or 1, which would be treated as a 'universally true' and a 'universally false' Boolean function, i.e. the least upper bound and the greatest lower bound of all the Boolean functions. Use is made of the partition of the Boolean matrices.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1965
Accession Number
AD0724782

Entities

People

  • Robert S. Ledley

Tags

DTIC Thesaurus Topics

  • Computer Programming
  • Computers
  • Digital Computers
  • Equations
  • Identities
  • Inclusions
  • Inspection
  • Maryland
  • Mathematics
  • New York
  • Notation
  • Observation
  • Permutations
  • Reasoning

Fields of Study

  • Computer science
  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Computer Programming and Software Development.