Category:Definitions/Reflection Matrices

This category contains definitions related to Reflection Matrices.
Related results can be found in Category:Reflection Matrices.

Let $\tuple {\mathbf e_1, \mathbf e_2, \mathbf e_3}$ be the orthonormal basis of a Cartesian coordinate system $C$ on (ordinary) space $S$.

Let $O$ be the origin of $C$.

Let $\tuple {\mathbf e'_1, \mathbf e'_2, \mathbf e'_3}$ be the orthonormal basis of another Cartesian coordinate system $C'$ on $S$, also with origin $O$ and with the same orientation as $C$.

The reflection matrix $R$ from $C$ to $C'$ is the square matrix of order $3$:

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where $a_{i j}$ is defined as:

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for $i, j \in \set {1, 2, 3}$.