# 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).