Rotatsioonimatiise
Rotatsioonimatiise, also known as rotational matrices, are mathematical tools used primarily in linear algebra and geometry to describe rotations in Euclidean space. These matrices represent linear transformations that rotate vectors in a coordinate system around an origin. In two-dimensional space, a rotation matrix rotates a point (x, y) around the origin by a specified angle θ, transforming it into a new position (x′, y′). The matrix takes the form:
When applied to a vector, the new coordinates are calculated by multiplying the matrix with the original
In three-dimensional space, rotations become more complex due to the additional axis of rotation. A general
Rotational matrices preserve lengths and angles, ensuring that geometric properties remain consistent after transformation. They are