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2. atan2 - Wikipedia

   en.wikipedia.org/wiki/Atan2

   In computing and mathematics, the function atan2 is the 2- argument arctangent. By definition, is the angle measure (in radians, with ) between the positive -axis and the ray from the origin to the point in the Cartesian plane. Equivalently, is the argument (also called phase or angle) of the complex number (The argument of a function and the ...

3. Direction cosine - Wikipedia

   en.wikipedia.org/wiki/Direction_cosine

   General meaning. More generally, direction cosine refers to the cosine of the angle between any two vectors. They are useful for forming direction cosine matrices that express one set of orthonormal basis vectors in terms of another set, or for expressing a known vector in a different basis. Simply put, direction cosines provide an easy method ...

4. Dot product - Wikipedia

   en.wikipedia.org/wiki/Dot_product

   Dot product. In mathematics, the dot product or scalar product[note 1] is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used. It is often called the inner product (or ...

5. Orthogonality (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Orthogonality_(mathematics)

   Orthogonality (mathematics) In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity to the linear algebra of bilinear forms. Two elements u and v of a vector space with bilinear form are orthogonal when . Depending on the bilinear form, the vector space may contain non-zero self-orthogonal vectors.

6. Cosine similarity - Wikipedia

   en.wikipedia.org/wiki/Cosine_similarity

   Cosine similarity. In data analysis, cosine similarity is a measure of similarity between two non-zero vectors defined in an inner product space. Cosine similarity is the cosine of the angle between the vectors; that is, it is the dot product of the vectors divided by the product of their lengths. It follows that the cosine similarity does not ...

7. Vector projection - Wikipedia

   en.wikipedia.org/wiki/Vector_projection

   Vector projection. The vector projection (also known as the vector component or vector resolution) of a vector a on (or onto) a nonzero vector b is the orthogonal projection of a onto a straight line parallel to b. The projection of a onto b is often written as or a∥b. The vector component or vector resolute of a perpendicular to b, sometimes ...

8. Rotation matrix - Wikipedia

   en.wikipedia.org/wiki/Rotation_matrix

   Rotation matrix. In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix. rotates points in the xy plane counterclockwise through an angle θ about the origin of a two-dimensional Cartesian coordinate system.

9. Vector algebra relations - Wikipedia

   en.wikipedia.org/wiki/Vector_algebra_relations

   The following are important identities in vector algebra.Identities that only involve the magnitude of a vector ‖ ‖ and the dot product (scalar product) of two vectors A·B, apply to vectors in any dimension, while identities that use the cross product (vector product) A×B only apply in three dimensions, since the cross product is only defined there.