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.







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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.







    share|cite|improve this question






















      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.







      share|cite|improve this question












      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.









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      asked Aug 28 at 14:12









      QuantumNik

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