Vector
A vector is an element of a vector space. In coordinates it can be represented by an ordered list of numbers with rules for addition and scalar multiplication.
Definition
A vector is an element of a vector space. In coordinates it can be represented by an ordered list of numbers with rules for addition and scalar multiplication.
Intuition
Coordinates describe a vector relative to a basis; changing basis changes the coordinates, not the underlying vector.
Worked example
Adding (1, 2) and (3, −1) gives (4, 1). Multiplying (1, 2) by 3 gives (3, 6).
The math
In , vector addition and scalar multiplication act coordinate by coordinate.
In machine learning
Vectors represent features, displacements, signals, and model parameters.
Go deeper
Sources
More in Linear algebra
Assembled from the ReLU.chat curated knowledge base. These explanations are concise on purpose; check the sources for anything important.