computing phase of complex matrix exponential times vector
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There are a real matrix $mathbbH$ and a real vector $R_1$. I need to calculate the following
$$C = exp(i mathbbH)R_1,$$
where the vector $C$ is, obviously, complex.
My question is if it is possible to represent the vector $C$ in the polar form, i.e. with components $R_2 exp(i S)_j$. By representation I mean some analytical formula which allows to calculate phase $S$ avoiding matrix exponentiation by taking logarithm or something similar. I feel there should be some simple way to do it but I can not find it.
complex-numbers matrix-equations matrix-exponential
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up vote
0
down vote
favorite
There are a real matrix $mathbbH$ and a real vector $R_1$. I need to calculate the following
$$C = exp(i mathbbH)R_1,$$
where the vector $C$ is, obviously, complex.
My question is if it is possible to represent the vector $C$ in the polar form, i.e. with components $R_2 exp(i S)_j$. By representation I mean some analytical formula which allows to calculate phase $S$ avoiding matrix exponentiation by taking logarithm or something similar. I feel there should be some simple way to do it but I can not find it.
complex-numbers matrix-equations matrix-exponential
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
There are a real matrix $mathbbH$ and a real vector $R_1$. I need to calculate the following
$$C = exp(i mathbbH)R_1,$$
where the vector $C$ is, obviously, complex.
My question is if it is possible to represent the vector $C$ in the polar form, i.e. with components $R_2 exp(i S)_j$. By representation I mean some analytical formula which allows to calculate phase $S$ avoiding matrix exponentiation by taking logarithm or something similar. I feel there should be some simple way to do it but I can not find it.
complex-numbers matrix-equations matrix-exponential
There are a real matrix $mathbbH$ and a real vector $R_1$. I need to calculate the following
$$C = exp(i mathbbH)R_1,$$
where the vector $C$ is, obviously, complex.
My question is if it is possible to represent the vector $C$ in the polar form, i.e. with components $R_2 exp(i S)_j$. By representation I mean some analytical formula which allows to calculate phase $S$ avoiding matrix exponentiation by taking logarithm or something similar. I feel there should be some simple way to do it but I can not find it.
complex-numbers matrix-equations matrix-exponential
asked Aug 28 at 14:12
QuantumNik
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