Determinant and Inverse of Matrices of Real Elements

Nobuyuki Tamura; Yatsuka Nakamura

Formalized Mathematics (2007)

  • Volume: 15, Issue: 3, page 127-136
  • ISSN: 1426-2630

Abstract

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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.

How to cite

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Nobuyuki Tamura, and Yatsuka Nakamura. "Determinant and Inverse of Matrices of Real Elements." Formalized Mathematics 15.3 (2007): 127-136. <http://eudml.org/doc/266534>.

@article{NobuyukiTamura2007,
abstract = {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.},
author = {Nobuyuki Tamura, Yatsuka Nakamura},
journal = {Formalized Mathematics},
language = {eng},
number = {3},
pages = {127-136},
title = {Determinant and Inverse of Matrices of Real Elements},
url = {http://eudml.org/doc/266534},
volume = {15},
year = {2007},
}

TY - JOUR
AU - Nobuyuki Tamura
AU - Yatsuka Nakamura
TI - Determinant and Inverse of Matrices of Real Elements
JO - Formalized Mathematics
PY - 2007
VL - 15
IS - 3
SP - 127
EP - 136
AB - 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.
LA - eng
UR - http://eudml.org/doc/266534
ER -

References

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