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 . 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.

Link to original

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