- #1

- 11

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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.

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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