Cayley-Hamilton theorem for left eigenvalues of 3 × 3 quaternionic matrices

E. Macías-Virgós; M.J. Pereira-Sáez

Special Matrices (2014)

  • Volume: 2, Issue: 1, page 11-18, electronic only
  • ISSN: 2300-7451

Abstract

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We prove that any quaternionic matrix of order n ≤3 admits a characteristic function, whose roots are the left eigenvalues, that satisfes Cayley-Hamilton theorem.

How to cite

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E. Macías-Virgós, and M.J. Pereira-Sáez. "Cayley-Hamilton theorem for left eigenvalues of 3 × 3 quaternionic matrices." Special Matrices 2.1 (2014): 11-18, electronic only. <http://eudml.org/doc/267239>.

@article{E2014,
abstract = {We prove that any quaternionic matrix of order n ≤3 admits a characteristic function, whose roots are the left eigenvalues, that satisfes Cayley-Hamilton theorem.},
author = {E. Macías-Virgós, M.J. Pereira-Sáez},
journal = {Special Matrices},
keywords = {Quaternionic matrix; left eigenvalue; characteristic function; Cayley-Hamilton theorem; quaternionic matrix},
language = {eng},
number = {1},
pages = {11-18, electronic only},
title = {Cayley-Hamilton theorem for left eigenvalues of 3 × 3 quaternionic matrices},
url = {http://eudml.org/doc/267239},
volume = {2},
year = {2014},
}

TY - JOUR
AU - E. Macías-Virgós
AU - M.J. Pereira-Sáez
TI - Cayley-Hamilton theorem for left eigenvalues of 3 × 3 quaternionic matrices
JO - Special Matrices
PY - 2014
VL - 2
IS - 1
SP - 11
EP - 18, electronic only
AB - We prove that any quaternionic matrix of order n ≤3 admits a characteristic function, whose roots are the left eigenvalues, that satisfes Cayley-Hamilton theorem.
LA - eng
KW - Quaternionic matrix; left eigenvalue; characteristic function; Cayley-Hamilton theorem; quaternionic matrix
UR - http://eudml.org/doc/267239
ER -

References

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  1. [1] Aslaksen, H. Quaternionic determinants. Math. Intell. 18, No. 3, 57-65 (1996). Zbl0881.15007
  2. [2] Cohen, N.; De Leo, S. The quaternionic determinant. Electron. J. Linear Algebra 7, 100-111 (2000). Zbl0977.15004
  3. [3] Gelfand, I.M.; Krob, D.; Lascoux, A.; Leclerc, B.; Retakh, V.; Thibon, J.-Y. Noncommutative symmetric functions. Adv. Math., 112, No. 2, 218-348 (1995).[Crossref][WoS] Zbl0831.05063
  4. [4] Gelfand, I.; Gelfand, S.; Retakh, V.; Lee Wilson R. Quasideterminants. Adv. Math. 193, No. 1, 56-141 (2005). Zbl1079.15007
  5. [5] Huang, L. On two questions about quaternion matrices. Linear Algebra Appl. 318, No. 1-3, 79-86 (2000). Zbl0965.15016
  6. [6] Macías-Virgós, E.; Pereira-Sáez, M.J. A topological approach to left eigenvalues of quaternionic matrices, Linear Multilinear Algebra 62, No. 2, 139-158 (2014).[WoS] Zbl1290.15010
  7. [7] Wood, R.M.W. Quaternionic eigenvalues. Bull. Lond. Math. Soc. 17, 137-138 (1985). Zbl0537.15011
  8. [8] Zhang, F. Quaternions and matrices of quaternions. Linear Algebra Appl. 251, 21-57 (1997). Zbl0873.15008
  9. [9] Zhang, F. Geršgorin type theorems for quaternionic matrices. Linear Algebra Appl. 424, No. 1, 139-153 (2007). [WoS] Zbl1117.15017

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