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July 3rd, 2015, 02:09 AM   #1
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From: Aalborg

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Specific solutions in the null space of a complex matrix

Hello, I'm dealing here with the following problem:
I have a complex matrix $\displaystyle F$, having size $\displaystyle N \times M$, with $\displaystyle N<<M$. I can easily compute a basis of the null space of $\displaystyle F$, i.e. the space of vectors $\displaystyle x$ such that $\displaystyle Fx=0_v$, where $\displaystyle 0_v$ denotes the $\displaystyle N \times 1$ column vector of all zeros.
However, I'm interested to specific solutions of the $\displaystyle Fx=0_v$ problem, i.e. to the vector(s) $\displaystyle x$ such that $\displaystyle \left|x_i\right|=1$ for $\displaystyle i=1,...,M$. I'm seeking vectors having constant amplitude.
Do you have any insights?
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