Hi;(adsbygoogle = window.adsbygoogle || []).push({});

How to raising a square matrix to the power of a complex number?

for example:

[1 2;3 4]^(1+i)

or mathematics software such as Scilab how solve such problems?

-->[1 2;3 4]^(1+%i)

ans =

- 0.1482039 - 0.2030943

- 0.3046414 - 0.4528453

Thanks in advance.

-----

Additational remark:

for element by element power operation (.^) , the output value is equal to the principle value computed as:

z1.^z2 = exp( z2* ( log(abs(z1)) + %i*atan(imag(z1)/real(z1)) ) )

-->[1 2;3 4].^(1+%i)

ans =

1. 1.5384778 + 1.2779226i

1.3644973 + 2.6717311i 0.7338279 + 3.932111i

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Square matrix to the power of a imaginary unit

Loading...

Similar Threads - Square matrix power | Date |
---|---|

I Trying to understand least squares estimates | Feb 25, 2017 |

I Why do eigenvectors stay the same when a matrix is squared? | Sep 11, 2016 |

Square root of matrix | Jan 18, 2016 |

Square of a permutation matrix | Feb 14, 2015 |

Finding powers of a square matrix | Mar 11, 2008 |

**Physics Forums - The Fusion of Science and Community**