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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  1. [1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990. 
  2. [2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990. 
  3. [3] Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990. 
  4. [4] Czesław Byliński. Binary operations applied to finite sequences. Formalized Mathematics, 1(4):643-649, 1990. 
  5. [5] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990. 
  6. [6] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990. 
  7. [7] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990. 
  8. [8] Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990. 
  9. [9] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991. 
  10. [10] Katarzyna Jankowska. Matrices. Abelian group of matrices. Formalized Mathematics, 2(4):475-480, 1991. 
  11. [11] Jarosław Kotowicz and Yatsuka Nakamura. Introduction to Go-board - part I. Formalized Mathematics, 3(1):107-115, 1992. 
  12. [12] Eugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990. 
  13. [13] Yatsuka Nakamura and Hiroshi Yamazaki. Calculation of matrices of field elements. Part I. Formalized Mathematics, 11(4):385-391, 2003. 
  14. [14] Library Committee of the Association of Mizar Users. Binary operations on numbers. To appear in Formalized Mathematics. 
  15. [15] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics. 
  16. [16] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990. 
  17. [17] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990. 
  18. [18] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990. 
  19. [19] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  20. [20] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990. 
  21. [21] Katarzyna Zawadzka. The sum and product of finite sequences of elements of a field. Formalized Mathematics, 3(2):205-211, 1992. 
  22. [22] Katarzyna Zawadzka. The product and the determinant of matrices with entries in a field. Formalized Mathematics, 4(1):1-8, 1993. 

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