@MISC{MATRIX14.MIZ,
  AUTHOR = {Nakamura, Yatsuka and Oniumi, Kunio and Chang, Wenpai},
  TITLE = {Invertibility of Matrices of Field Elements},
  SECTION1 = {Preparation},
  SECTION2 = {Zero Vector and Base Vectors of Field Elements},
  SECTION3 = {Conditions of Invertibility},
  SECTION4 = {A Transformation of Matrix to Some Canonical Form},
  SECTION5 = {Left/Right Invertibility and Invertibility},
  DAY = {2},
  MONTH = {April},
  YEAR = {2008},
  ADDRESS1 = {Shinshu University\\Nagano, Japan},
  ADDRESS2 = {Shinshu University\\Nagano, Japan},
  ADDRESS3 = {Nan Kai Institute of Technology\\Nantou County, Taiwan},
  SUMMARY = {In this paper the theory of invertibility of
  matrices of field elements (see e.g. \cite{Furuya:57},
  \cite{Gantmacher:59})
  is developed. The main purpose of this article is to prove that
  the left invertibility and the right invertibility are equivalent
  for a matrix of field elements.
  To prove this, we introduced a special transformation of
  matrix to some canonical form.
  Other concepts as zero vector and base vectors of field
  elements are also introduced as a preparation.}}

