@MISC{MATRIXR2.MIZ,
  AUTHOR = {Tamura, Nobuyuki and Nakamura, Yatsuka},
  TITLE = {Determinant and Inverse of Matrices of Real Elements},
  SECTION1 = {Preliminaries},
  SECTION2 = {Calculation of Matrices},
  SECTION3 = {Determinants},
  SECTION4 = {Matrix as Operator},
  SECTION5 = {Identity and Zero of Matrix of $\BbbR$},
  SECTION6 = {Inverse of Matrix},
  DAY = {17},
  MONTH = {July},
  YEAR = {2007},
  ADDRESS1 = {Shinshu University\\Nagano, Japan},
  ADDRESS2 = {Shinshu University\\Nagano, Japan},
  SUMMARY = {In this paper the classic theory of matrices of real elements
  (see e.g. \cite{Furuya57}, cite{Gantmacher:59})
  is developed. We prove selected equations that have been proved previously
  for matrices of field elements. Similarly, we introduce in this
  special context the determinant of a matrix, the identity and zero matrices, and
  the inverse matrix.
  The new concept discussed in the case of matrices of real numbers is
  the property of matrices as operators acting on finite sequences of
  real numbers from both sides.
  The relations of invertibility of matrices and the ``onto"
  property of matrices as operators are discussed.}}

@BOOK{Furuya:57,
       AUTHOR = {Furuya, Shigeru},
        TITLE = {Matrix and Determinant},
    PUBLISHER = {Baifuukan},
          EAR = {1957},
         NOTE = {in Japanese}}

@BOOK{Gantmacher:59,
        AUTHOR = {Gantmacher, Felix R.},
         TITLE = {The Theory of Matrices},
     PUBLISHER = {AMS Chelsea Publishing},
          YEAR = {1959}}


