General Form of 3x3 unitary matrix

1. Feb 9, 2008

emob2p

Hi,

Does anyone know the general form of a 3x3 Unitary Matrix? I know for 2x2 it can be parametrized by 2 complex numbers. I remember once seeing a general form for the 3x3 in terms of 6, I think, complex numbers. Anyway, I'm having trouble finding that now...so if anyone could help me it would be greatly appreciated.

Thanks,
Eric

2. Feb 9, 2008

morphism

I'm not sure if this is what you mean, but any nxn unitary matrix is similar to a matrix of the form

$$\left(\begin{array}{ccc} e^{i \theta_1} & & 0 \\ & \ddots & \\ 0 & & e^{i \theta_n} \end{array}\right)$$

This is because a unitary matrix is diagonalizable and its eigenvalues all lie on the unit circle (i.e. have absolute value 1).

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?