A Theory of Matrices of Real Elements

Yatsuka Nakamura; Nobuyuki Tamura; Wenpai Chang

Formalized Mathematics (2006)

  • Volume: 14, Issue: 1, page 21-28
  • ISSN: 1426-2630

Abstract

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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.

How to cite

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Yatsuka Nakamura, Nobuyuki Tamura, and Wenpai Chang. "A Theory of Matrices of Real Elements." Formalized Mathematics 14.1 (2006): 21-28. <http://eudml.org/doc/267519>.

@article{YatsukaNakamura2006,
abstract = {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.},
author = {Yatsuka Nakamura, Nobuyuki Tamura, Wenpai Chang},
journal = {Formalized Mathematics},
language = {eng},
number = {1},
pages = {21-28},
title = {A Theory of Matrices of Real Elements},
url = {http://eudml.org/doc/267519},
volume = {14},
year = {2006},
}

TY - JOUR
AU - Yatsuka Nakamura
AU - Nobuyuki Tamura
AU - Wenpai Chang
TI - A Theory of Matrices of Real Elements
JO - Formalized Mathematics
PY - 2006
VL - 14
IS - 1
SP - 21
EP - 28
AB - 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.
LA - eng
UR - http://eudml.org/doc/267519
ER -

References

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