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Let's say we have a complex eigenvector (v) as a result of a natural frequency calculation of multi DoF system. I'm wondering what kind of physical meaning has the cross product of Re(v) $\times$ Im(v).

Thank's for the answer in advance

  • Presumably you’re working in $\mathbb R^3$ (or perhaps $\mathbb R^2$) since you have a cross product at all to ask about. Think about the plane spanned by the real and imaginary parts of $\mathbf v$ and how it relates to the scaled rotation represented by the complex eigenvalues. – amd Jul 12 '19 at 09:40
  • Yes indeed i forgot to add that i'm talking about $\mathbb{R}^3$ –  Jul 12 '19 at 10:12
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    Effectively a duplicate of https://math.stackexchange.com/q/1546104/265466. The real and imaginary parts of $\mathbf v$ span the plane of the (scaled) rotation, so in $\mathbb R^3$ their cross product defines the corresponding rotation axis. The length of this cross product is pretty much meaningless since you can scale an eigenvector arbitrarily. – amd Jul 12 '19 at 18:36

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