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2. Euclidean vector - Wikipedia

   en.wikipedia.org/wiki/Euclidean_vector

   All examples thus far have dealt with vectors expressed in terms of the same basis, namely, the e basis {e 1, e 2, e 3}. However, a vector can be expressed in terms of any number of different bases that are not necessarily aligned with each other, and still remain the same vector.

3. Vector (mathematics and physics) - Wikipedia

   en.wikipedia.org/wiki/Vector_(mathematics_and...

   A vector pointing from A to B. In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector [1] or spatial vector [2]) is a geometric object that has magnitude (or length) and direction. Euclidean vectors can be added and scaled to form a vector space. A vector quantity is a vector-valued ...

4. Free module - Wikipedia

   en.wikipedia.org/wiki/Free_module

   Free module. In mathematics, a free module is a module that has a basis, that is, a generating set consisting of linearly independent elements. Every vector space is a free module, [1] but, if the ring of the coefficients is not a division ring (not a field in the commutative case), then there exist non-free modules.

5. Vector space - Wikipedia

   en.wikipedia.org/wiki/Vector_space

   Below, w is stretched by a factor of 2, yielding the sum v + 2w. In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, can be added together and multiplied ("scaled") by numbers called scalars. The operations of vector addition and scalar multiplication must satisfy certain ...

6. Couple (mechanics) - Wikipedia

   en.wikipedia.org/wiki/Couple_(mechanics)

   Classical mechanics. In physics, a couple is a system of forces with a resultant (a.k.a. net or sum) moment of force but no resultant force. [1] A more descriptive term is force couple or pure moment. Its effect is to impart angular momentum but no linear momentum. In rigid body dynamics, force couples are free vectors, meaning their effects on ...

7. Kernel (linear algebra) - Wikipedia

   en.wikipedia.org/wiki/Kernel_(linear_algebra)

   Kernel (linear algebra) In mathematics, the kernel of a linear map, also known as the null space or nullspace, is the part of the domain which is mapped to the zero vector of the co-domain; the kernel is always a linear subspace of the domain. [1] That is, given a linear map L : V → W between two vector spaces V and W, the kernel of L is the ...