@MISC{MATRIXR1.MIZ,
  AUTHOR = {Nakamura, Yatsuka and Tamura, Nobuyuki and Chang, Wenpai},
  TITLE = {A Theory of Matrices of Real Elements},
  SECTION1 = {Preliminaries},
  SECTION2 = {Matrices of Real Elements},
  DAY = {20},
  MONTH = {February},
  YEAR = {2006},
  ADDRESS1 = {Shinshu University\\Nagano, Japan},
  ADDRESS2 = {Shinshu University\\Nagano, Japan},
  ADDRESS3 = {Shinshu University\\Nagano, Japan},
  SUMMARY = {Here, the concept of matrix of real elements
  is introduced. This is defined as a special case of
  the general concept of matrix of a field.
  For such a real matrix, the notions of addition, subtraction,
  scalar product are defined. For any real finite sequences,
  two transformations to matrices are introduced. One of the
  matrices is of width 1, and the other is of length 1.
  By such transformations, two products of a matrix and
  a finite sequence are defined. Also the linearity of
  such product is shown.}}

