Hi friends, in mathematics, today we will discuss about Rotation Matrix. And also we will study different method to solve the rotation matrix. Generally a rotation matrix is used to show a rotation in linear algebra. For example:
p = [ cos Ф - sin Ф]
[ sin Ф cos Ф]
In the matrix mention above matrix points are rotated in xy – Cartesian plane ( here x is along to horizontal axis and y is along to vertical axis) through an angle Ф about the origin of coordinate system. Using the matrix multiplication we also found a rotated vector. So there is no effect of multiplication on zero vector or in other word it can be a coordinates of the origin. Commonly rotation matrix is used to calculate rotations about the origin of coordinate system. It can also be used to assist a simple algebraic description of such types of rotations and it can also be used for computation in physics, geometric, etc. If we talk about the case of three dimensional space then the rotation can be stop by given angle along a single axis of rotation. So, it can be simply calculated by an angle and vector by three entries. In case of 3x3 Rotation Matrix. It can be solved by nine entries of a rotation matrix that has three rows and three columns. It can not be used in higher dimensions. (know more about Rotation Matrix, here)
It is also said to be orthogonal matrices that has determinant value is equal to 1. It can be denoted as:
= Pa = P-1, det P = 1. this type of matrices are called as special orthogonal group. It can be denoted as 'SO (n). Entire rotational matrices are found using these matrix multiplication. For example:
= Pp (γ) Pq (β) Pr (α); it can be denoted as a rotation whose angles are α, β, γ. This is all about rotation Matrix.
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