IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v311y2017icp375-389.html
   My bibliography  Save this article

Multivector and multivector matrix inverses in real Clifford algebras

Author

Listed:
  • Hitzer, Eckhard
  • Sangwine, Stephen

Abstract

We show how to compute the inverse of multivectors in finite dimensional real Clifford algebras Cl(p, q). For algebras over vector spaces of fewer than six dimensions, we provide explicit formulae for discriminating between divisors of zero and invertible multivectors, and for the computation of the inverse of a general invertible multivector. For algebras over vector spaces of dimension six or higher, we use isomorphisms between algebras, and between multivectors and matrix representations with multivector elements in Clifford algebras of lower dimension. Towards this end we provide explicit details of how to compute several forms of isomorphism that are essential to invert multivectors in arbitrarily chosen algebras. We also discuss briefly the computation of the inverses of matrices of multivectors by adapting an existing textbook algorithm for matrices to the multivector setting, using the previous results to compute the required inverses of individual multivectors.

Suggested Citation

  • Hitzer, Eckhard & Sangwine, Stephen, 2017. "Multivector and multivector matrix inverses in real Clifford algebras," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 375-389.
    • Handle: RePEc:eee:apmaco:v:311:y:2017:i:c:p:375-389
    DOI: 10.1016/j.amc.2017.05.027
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300317303259
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2017.05.027?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Li, Lixing, 2011. "The incentive role of creating "cities" in China," China Economic Review, Elsevier, vol. 22(1), pages 172-181, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wei Tang & Geoffrey J.D. Hewings, 2017. "Do city–county mergers in China promote local economic development?," The Economics of Transition, The European Bank for Reconstruction and Development, vol. 25(3), pages 439-469, July.
    2. Mukim,Megha & Zhu,Tingting Juni, 2015. "Empowering cities : good for growth ? evidence from China," Policy Research Working Paper Series 7193, The World Bank.
    3. Che, Jiahua & Chung, Kim-Sau & Lu, Yang K., 2017. "Decentralization and political career concerns," Journal of Public Economics, Elsevier, vol. 145(C), pages 201-210.
    4. John Knight, 2015. "The Principal-Agent Problem, Economic Growth, Subjective Wellbeing and Social Instability: China’s Effective but Flawed Governance," Economics Series Working Papers 758, University of Oxford, Department of Economics.
    5. Caldeira, Emilie, 2012. "Yardstick competition in a federation: Theory and evidence from China," China Economic Review, Elsevier, vol. 23(4), pages 878-897.
    6. Che, Yi, 2009. "Mismatch: land reallocations, recovery land rental and land rental market development in rural China," MPRA Paper 39794, University Library of Munich, Germany.
    7. Tie-Ying Liu & Chi-Wei Su & Xu-Zhao Jiang, 2016. "Is China’S Urbanization Convergent?," The Singapore Economic Review (SER), World Scientific Publishing Co. Pte. Ltd., vol. 61(05), pages 1-18, December.
    8. Megha Mukim & T. Juni Zhu, 2018. "Empowering Cities: Good for Growth? Evidence from the People's Republic of China," Asian Development Review, MIT Press, vol. 35(1), pages 175-195, March.
    9. Ruiz-Lozano, Mercedes & Tirado-Valencia, Pilar, 2016. "Do industrial companies respond to the guiding principles of the Integrated Reporting framework? A preliminary study on the first companies joined to the initiative," Revista de Contabilidad - Spanish Accounting Review, Elsevier, vol. 19(2), pages 252-260.
    10. Lixing Li & Guangrong Ma, 2015. "Government Size and Tax Evasion: Evidence from China," Pacific Economic Review, Wiley Blackwell, vol. 20(2), pages 346-364, May.
    11. Fan, Shenggen & Li, Lixing & Zhang, Xiaobo, 2012. "Challenges of creating cities in China: Lessons from a short-lived county-to-city upgrading policy," Journal of Comparative Economics, Elsevier, vol. 40(3), pages 476-491.
    12. Chenggang Xu, 2011. "The Fundamental Institutions of China's Reforms and Development," Journal of Economic Literature, American Economic Association, vol. 49(4), pages 1076-1151, December.
    13. Xu, Cheng-Gang, 2010. "The Institutional Foundations of China?s Reforms and Development," CEPR Discussion Papers 7654, C.E.P.R. Discussion Papers.
    14. Chao Li & John Gibson, 2016. "Pareto's Law and City Size in China: Diverging Patterns in Land and People," Working Papers in Economics 16/09, University of Waikato.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:311:y:2017:i:c:p:375-389. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.