Home > Research > Publications & Outputs > Orthogonal invariants of a matrix of order four...

Research

Associated organisational unit

Links

Text available via DOI:

View graph of relations

Orthogonal invariants of a matrix of order four and applications

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Published

Standard

Orthogonal invariants of a matrix of order four and applications. / Đoković, Dragomir; MacDonald, Mark.
In: Journal of Pure and Applied Algebra, Vol. 202, No. 1-3, 01.11.2005, p. 259-283.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Đoković, D & MacDonald, M 2005, 'Orthogonal invariants of a matrix of order four and applications', Journal of Pure and Applied Algebra, vol. 202, no. 1-3, pp. 259-283. https://doi.org/10.1016/j.jpaa.2005.02.011

APA

Đoković, D., & MacDonald, M. (2005). Orthogonal invariants of a matrix of order four and applications. Journal of Pure and Applied Algebra, 202(1-3), 259-283. https://doi.org/10.1016/j.jpaa.2005.02.011

Vancouver

Đoković D, MacDonald M. Orthogonal invariants of a matrix of order four and applications. Journal of Pure and Applied Algebra. 2005 Nov 1;202(1-3):259-283. doi: 10.1016/j.jpaa.2005.02.011

Author

Đoković, Dragomir ; MacDonald, Mark. / Orthogonal invariants of a matrix of order four and applications. In: Journal of Pure and Applied Algebra. 2005 ; Vol. 202, No. 1-3. pp. 259-283.

Bibtex

@article{26d76a8922284c658ab707ace9600778,
title = "Orthogonal invariants of a matrix of order four and applications",
abstract = "We determine explicitly the algebras of SO4(C)-invariants and O4(C)-invariants of a traceless matrix A of order 4, i.e., we find a set of homogeneous system parameters, minimal set of algebra generators, and Hironaka decomposition for each of these algebras. We have also computed the Hilbert series for the algebra of SOn(C)-invariants of a single matrix A of order n⩽6. All this was originally motivated by the question of orthogonal tridiagonalizability of real matrices of order 4. We show that the answer to this question is negative. It is also negative in the case of complex matrices of order 4 acted upon by the usual complex orthogonal group O4(C).",
author = "Dragomir {\D}okovi{\'c} and Mark MacDonald",
year = "2005",
month = nov,
day = "1",
doi = "10.1016/j.jpaa.2005.02.011",
language = "English",
volume = "202",
pages = "259--283",
journal = "Journal of Pure and Applied Algebra",
issn = "0022-4049",
publisher = "Elsevier",
number = "1-3",

}

RIS

TY - JOUR

T1 - Orthogonal invariants of a matrix of order four and applications

AU - Đoković, Dragomir

AU - MacDonald, Mark

PY - 2005/11/1

Y1 - 2005/11/1

N2 - We determine explicitly the algebras of SO4(C)-invariants and O4(C)-invariants of a traceless matrix A of order 4, i.e., we find a set of homogeneous system parameters, minimal set of algebra generators, and Hironaka decomposition for each of these algebras. We have also computed the Hilbert series for the algebra of SOn(C)-invariants of a single matrix A of order n⩽6. All this was originally motivated by the question of orthogonal tridiagonalizability of real matrices of order 4. We show that the answer to this question is negative. It is also negative in the case of complex matrices of order 4 acted upon by the usual complex orthogonal group O4(C).

AB - We determine explicitly the algebras of SO4(C)-invariants and O4(C)-invariants of a traceless matrix A of order 4, i.e., we find a set of homogeneous system parameters, minimal set of algebra generators, and Hironaka decomposition for each of these algebras. We have also computed the Hilbert series for the algebra of SOn(C)-invariants of a single matrix A of order n⩽6. All this was originally motivated by the question of orthogonal tridiagonalizability of real matrices of order 4. We show that the answer to this question is negative. It is also negative in the case of complex matrices of order 4 acted upon by the usual complex orthogonal group O4(C).

U2 - 10.1016/j.jpaa.2005.02.011

DO - 10.1016/j.jpaa.2005.02.011

M3 - Journal article

VL - 202

SP - 259

EP - 283

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 1-3

ER -