Perusrotaatiomatriisit
Perusrotaatiomatriisit, or basic rotation matrices, are fundamental tools in linear algebra and geometry, used to represent rotations in two-dimensional space. A rotation matrix is a 2x2 matrix that, when multiplied by a vector, rotates the vector by a specified angle around the origin. The general form of a 2D rotation matrix is:
where θ is the angle of rotation in radians. This matrix performs a counterclockwise rotation when θ is
The determinant of a rotation matrix is always 1, indicating that the transformation preserves the area of
In three-dimensional space, rotation matrices are represented by 3x3 matrices. These matrices can describe rotations around
where θ is the angle of rotation. Similar matrices can be derived for rotations around the x and
Rotation matrices are widely used in various scientific and engineering disciplines due to their simplicity and