Given four complex quantities $\alpha, \beta,\gamma,\delta$ which satisfy the condition $\alpha\delta - \beta \gamma = 1$. What does it exactly mean that the four complex quantities under this condition are equivalent to 6 real parameters?
What means that four complex quantities under a condition are equivalent to 6 real parameters?
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linear-algebra
matrices
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0What do you mean with "equivalent"? Perhaps that when writing the complex numbers as pairs of real numbers we obtain two conditions (real part =1, imaginary part=0) from the equation? – 2017-02-11
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Four complex numbers are defined by eight parameters, four real parts and four imaginary parts. But the condition given: $\alpha \delta - \beta \gamma = 1 = 1 + 0i$ gives two parameters, so if you know six of the original parameters plus this condition you would be able to find the other two.