Angle between vectors in complex space

**dimper129** · November 18th 2010, 08:35 AM

Hi all,

How can I find the angle between two complex vectors? for example

$\begin{bmatrix}-0.8187 + 0.0000i \\-0.1488 - 0.0089i \\ -0.0266 + 0.0167i \\ 0.5010 + 0.2166i \\ -0.0886 + 0.0264i \end{bmatrix}<br /> <br /> \begin{bmatrix}-0.1510 + 0.0000i \\-0.0257 + 0.0195i \\ 0.5214 + 0.1720i \\ -0.8147 + 0.0624i \\ 0.0827 + 0.0185i \end{bmatrix}$

Thanks

**Ackbeet** · November 18th 2010, 09:05 AM

Using the dot product defined as

$\displaystyle\langle x,y\rangle=\sum_{k=1}^{n}x_{k}\bar{y}_{n},$

try this formula:

$\langle x,y\rangle=\sqrt{\langle x,x\rangle}\sqrt{\langle y,y\rangle}\,\cos(\theta).$

**HallsofIvy** · November 18th 2010, 11:34 AM

Of course, in complex space, you cannot expect the "angle" to be a real number.

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