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Mathematics-Online lexicon: Annotation to

Principal Axis Transformation

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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$.


The columns of the rotation matrix $ U$ contain the eigenvectors $ u_i$ of $ A$ the directions of which are called principal axes.

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  automatisch erstellt am 19.  8. 2013