2Dpöörlemismaatriks

2Dpöörlemismaatriks, also known as a 2D rotation matrix, is a fundamental concept in linear algebra and computer graphics. It is a 2x2 matrix used to perform rotations in a two-dimensional space. The general form of a 2D rotation matrix is:

[ cos(θ) -sin(θ) ]

[ sin(θ) cos(θ) ]

where θ is the angle of rotation in radians. This matrix can be used to rotate a point (x, y) around the origin by multiplying the matrix with the point's coordinates:

[ cos(θ) -sin(θ) ] * [ x ] = [ x' ]

[ sin(θ) cos(θ) ] [ y ] [ y' ]

The resulting coordinates (x', y') represent the new position of the point after rotation. The rotation matrix has several useful properties, including orthogonality and determinant equal to 1, which means it preserves the lengths of vectors and the orientation of the coordinate system. It is widely used in various applications, such as computer graphics, image processing, and robotics, to perform transformations and manipulations in a 2D space.