LINEAR ALGEBRA II es
Orthogonal maps
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LINEAR ALGEBRA II es |
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Orthogonal maps |
| Orthogonal maps in $\mathbb{R}^2$. | |
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An orthogonal transformation is an endormorphism
that preserves the dot product, and therefore angles and distances. A
transformation is direct if it preserves orientation and inverse
otherwise. In the following interactive graphics you can study the orthogonal maps of the vector space: $\mathbb{R}^2$. In this case there are only two types of orthogonal maps: - Rotations (direct transformations). - Symmetries respect to a line (inverse transformations). The composition of orthogonal maps is again an orthogonal map. In particular: - The composition or two rotations is a rotation. - The composition of a rotation and a symmetry is a symmetry - The compositiono of two symmetries is a rotation.
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School of Civil Engineering
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Universidade
da Coruña |
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Academic Year 2024/2025 |
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