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Formalized Mathematics

(a computer assisted approach)

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Volume 15, Issue 3 (Jan 2007)


Determinant and Inverse of Matrices of Real Elements

Nobuyuki Tamura
  • Shinshu University, Nagano, Japan
/ Yatsuka Nakamura
  • Shinshu University, Nagano, Japan
Published Online: 2008-06-09 | DOI: https://doi.org/10.2478/v10037-007-0014-7

Determinant and Inverse of Matrices of Real Elements

In this paper the classic theory of matrices of real elements (see e.g. [12], [13]) 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.

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About the article

Published Online: 2008-06-09

Published in Print: 2007-01-01

Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-007-0014-7. Export Citation

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