, Volume 54, Issue 3, pp 643–656 | Cite as

Square roots of \({3\times 3}\) matrices

  • Mehdi Ashkartizabi
  • Mina Aminghafari
  • Adel Mohammadpour


We find square roots of a complex-valued matrix \(A_{3 \times 3}\) using equation \(B^{2}=A\). The proposed method is faster than Higham’s method and provides up to 8 square roots with less relative residual and error.


Schur algorithm Square roots Cayley–Hamilton theorem 

Mathematics Subject Classification



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Copyright information

© Springer-Verlag Italia 2016

Authors and Affiliations

  • Mehdi Ashkartizabi
    • 1
  • Mina Aminghafari
    • 1
  • Adel Mohammadpour
    • 1
  1. 1.Department of Statistics, Faculty of Mathematics and Computer ScienceAmirkabir University of Technology (Tehran Polytechnic)TehranIran

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