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Determinant and Inverse of Matrices of Real Elements Cover

Determinant and Inverse of Matrices of Real Elements

Formalized Mathematics
Volume 15 (2007): Issue 3 (September 2007)
By: Nobuyuki Tamura and  Yatsuka Nakamura  
Open Access
|Jun 2008

References

  1. [1] Kanchun and Yatsuka Nakamura. The inner product of finite sequences and of points of n-dimensional topological space. Formalized Mathematics, 11(2):179-183, 2003.
    Search in Google Scholar
  2. [2] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
    Search in Google Scholar
  3. [3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
    Search in Google Scholar
  4. [4] Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.
    Search in Google Scholar
  5. [5] Czesław Byliński. Binary operations applied to finite sequences. Formalized Mathematics, 1(4):643-649, 1990.
    Search in Google Scholar
  6. [6] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.
    Search in Google Scholar
  7. [7] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
    Search in Google Scholar
  8. [8] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
    Search in Google Scholar
  9. [9] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
    Search in Google Scholar
  10. [10] Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.
    Search in Google Scholar
  11. [11] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.
    Search in Google Scholar
  12. [12] Shigeru Furuya. Matrix and Determinant. Baifuukan (in Japanese), 1957.
    Search in Google Scholar
  13. [13] Felix R. Gantmacher. The Theory of Matrices. AMS Chelsea Publishing, 1959.
    Search in Google Scholar
  14. [14] Katarzyna Jankowska. Matrices. Abelian group of matrices. Formalized Mathematics, 2(4):475-480, 1991.
    Search in Google Scholar
  15. [15] Katarzyna Jankowska. Transpose matrices and groups of permutations. Formalized Mathematics, 2(5):711-717, 1991.
    Search in Google Scholar
  16. [16] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.
    Search in Google Scholar
  17. [17] Eugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.
    Search in Google Scholar
  18. [18] Yatsuka Nakamura. Determinant of some matrices of field elements. Formalized Mathematics, 14(1):1-5, 2006.10.2478/v10037-006-0001-4
    Search in Google Scholar
  19. [19] Yatsuka Nakamura, Nobuyuki Tamaura, and Wenpai Chang. A theory of matrices of real elements. Formalized Mathematics, 14(1):21-28, 2006.10.2478/v10037-006-0004-1
    Search in Google Scholar
  20. [20] Yatsuka Nakamura and Hiroshi Yamazaki. Calculation of matrices of field elements. Part I. Formalized Mathematics, 11(4):385-391, 2003.
    Search in Google Scholar
  21. [21] Library Committee of the Association of Mizar Users. Binary operations on numbers. To appear in Formalized Mathematics.
    Search in Google Scholar
  22. [22] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics.
    Search in Google Scholar
  23. [23] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.
    Search in Google Scholar
  24. [24] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990.
    Search in Google Scholar
  25. [25] Andrzej Trybulec and Agata Darmochwał. Boolean domains. Formalized Mathematics, 1(1):187-190, 1990.
    Search in Google Scholar
  26. [26] Wojciech A. Trybulec. Binary operations on finite sequences. Formalized Mathematics, 1(5):979-981, 1990.
    Search in Google Scholar
  27. [27] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.
    Search in Google Scholar
  28. [28] Wojciech A. Trybulec. Pigeon hole principle. Formalized Mathematics, 1(3):575-579, 1990.
    Search in Google Scholar
  29. [29] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
    Search in Google Scholar
  30. [30] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
    Search in Google Scholar
  31. [31] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
    Search in Google Scholar
  32. [32] Hiroshi Yamazaki, Yoshinori Fujisawa, and Yatsuka Nakamura. On replace function and swap function for finite sequences. Formalized Mathematics, 9(3):471-474, 2001.
    Search in Google Scholar
  33. [33] Xiaopeng Yue, Xiquan Liang, and Zhongpin Sun. Some properties of some special matrices. Formalized Mathematics, 13(4):541-547, 2005.
    Search in Google Scholar
  34. [34] Katarzyna Zawadzka. The product and the determinant of matrices with entries in a field. Formalized Mathematics, 4(1):1-8, 1993.
    Search in Google Scholar
  35. [35] Bo Zhang and Yatsuka Nakamura. The definition of finite sequences and matrices of probability, and addition of matrices of real elements. Formalized Mathematics, 14(3):101-108, 2006.10.2478/v10037-006-0012-1
    Search in Google Scholar
DOI: https://doi.org/10.2478/v10037-007-0014-7 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
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Language: English
Page range: 127 - 136
Published on: Jun 9, 2008
Published by: University of Białystok
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Related subjects:
Computer sciences,
Computer sciences, other,
Mathematics,
General mathematics

© 2008 Nobuyuki Tamura, Yatsuka Nakamura, published by University of Białystok
This work is licensed under the Creative Commons License.

Volume 15 (2007): Issue 3 (September 2007)