THE LINEAR EQUATIONS PROBLEM.
APPLIED MATHEMATICS AND STATISTICS LABS STANFORD UNIV CALIF
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The simplest case of a linear equations problem is that of finding m unknowns by solving m linear algebraic non-homogeneous equations with given coefficients and constant terms. If this solution is carried out m times with the columns of the identity matrix as successive choices for the constant vector, the resulting sets of solutions form the columns of the inverse of the matrix coefficients. Another situation which is disposed of very simply in a purely theoretical treatment but which is non-trivial in practice is that in which there are more equations than unknowns, yet a solution is known, or at least believed, to exist. The purpose of the present paper is to describe a method of solving in a routine way a class of linear algebraic problems which include the various special cases mentioned.
- Theoretical Mathematics