LINEAR ALGEBRA II es
Orthogonal maps
|
|
LINEAR ALGEBRA II es |
|
|
Orthogonal maps |
| Orthogonal maps in $\mathbb{R}^2$. | |
|
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.
|
|
|
|
School of Civil Engineering
|
|
Universidade
da Coruña |
|
Academic Year 2023/2024 |
|
 |
| _______________________________________________________________________________________________________________________________ |
