- #1
sunny110
- 11
- 0
Hi;
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
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