An element of a Vector Space, represented in that space either by a direction and magnitude, or by a list of Numbers, each describing the placement along a coordinate axis.
Vector Space Element
Note that Vectors need not be
Link to original. Any possible element of a vector space is by definition, a vector. This means that vector spaces really contain Tensors. 99% of the time when people are talking about vectors, they really mean “Coordinate vector”, i.e. a vector that represents a location in Space. Whereas a vector represents a location in a Vector Space.
Operations
Addition
Add elementwise.
Subtraction
Subtract elementwise.
Scalar Multiplication
Multiply elementwise.
Magnitude
The magntiude calculates the distance from the tip of the vector to the origin.
Dot Product
Transclude of Dot-Product
Cross Product
Transclude of Cross-Product