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physicsXS
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where can I find a good article about a riguros description of matrix rotations? I can't find anything on PF...
A matrix rotation is a mathematical operation where a matrix is multiplied by a rotation matrix to transform the coordinates of points in a plane or space. This is used to rotate objects in 2D or 3D graphics and animations.
A rotation matrix is a special type of matrix that has specific properties to perform rotations. It is usually a square matrix with a determinant of 1, and its columns and rows are orthogonal unit vectors. In contrast, a regular matrix can have any size and properties, and it is used for various mathematical operations.
Matrix rotations have various applications in fields such as computer graphics, robotics, physics, and engineering. They are used to rotate and manipulate objects in 2D and 3D space, perform transformations in computer graphics, and solve problems in mechanics and kinematics.
The order of matrix multiplication is essential in matrix rotations because it determines the direction and axis of rotation. When multiplying a point by a rotation matrix, the order of multiplication follows the right-hand rule, where the rotation matrix is multiplied first, followed by the point's coordinates.
Quaternions are a mathematical concept that extends the properties of complex numbers to four dimensions. They are often used to represent rotations in 3D space, and they have advantages over matrix rotations, such as avoiding gimbal lock and performing smooth interpolations. However, quaternions can also be converted to rotation matrices and vice versa to achieve the same results.