Mathematics-Online lexicon: Principal Axis Transformation

	[home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff]
	Mathematics-Online lexicon:
	Principal Axis Transformation

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

By coordinate transformation (rotation and translation) a quadric in $\mathbb{R}^n$ can be brought to normal form:

$\displaystyle x^{\operatorname t}A x + 2 b^{\operatorname t}x + c = \sum_{i=1}^m \lambda_i w_i^2 + 2\beta w_{m+1} + \gamma \,,$

where $\beta\gamma=0$ .

$\includegraphics[width=\moimagesize]{a_hauptachsentrafo}$

The columns of the rotation matrix contain the eigenvectors of the directions of which are called principal axes.

see also:

automatically generated 7/13/2018