DataTerminology.comNEW
Also known as: Feature Vector
An ordered one-dimensional array representing quantities, often encoding magnitude and direction or numeric features.
DESCRIPTION
In mathematics, a vector is an entity with magnitude and direction, or more generally an element of a vector space. In data science and AI, vectors represent feature sets, embeddings, and parameters. Operations like addition, scaling, dot products, and norms underpin similarity, optimization, and projections. Implementation varies between row and column conventions, but semantics remain consistent. Vectors are foundational in linear algebra, geometry, signal processing, and machine learning.
ALTERNATIVE DEFINITIONS
Encyclopaedia Britannica
vector, in mathematics, a quantity that has magnitude and direction.
Stresses geometric interpretation central to physics and engineering.
Wolfram MathWorld
A vector is an element of a vector space.
Formal definition emphasizing algebraic structure.
RELATED TERMS
Matrix Tensor Dot Product Norm Embeddings Eigenvectors Gradient Linear Algebra Dissimilarity Measure
COMPETING TERMS
Scalar
RELATIONS
- Narrower: Dense Vector Initialization Vector Sparse Vector
KNOWLEDGE AREAS
Mathematics Data Science AI Programming Languages
TARGET AUDIENCE
Data Scientist AI Engineer Data Engineer Software Developer Data Modeler
EXTERNAL SOURCES
- Wikipedia - Vector (mathematics and physics)
- MIT OpenCourseWare - Foundational linear algebra course
- NumPy - Linear algebra operations for vectors
TOP QUESTIONS
Why are vectors fundamental in machine learning?
They encode features, parameters, and gradients, enabling efficient computation of similarity, distances, and optimization. Many algorithms reduce to linear algebra over vectors and matrices.
Category: Relevancy
What is the difference between a vector and a scalar?
A scalar has magnitude only, while a vector has magnitude and direction. In computations, vectors are ordered lists; scalars are single values.
Category: Misunderstanding
How do embeddings relate to vectors?
Embeddings are learned vectors representing entities (e.g., words, products) in a continuous space, capturing relationships through distances and directions.
Category: Application
What operations are common on vectors?
Addition, scalar multiplication, dot and cross products (in 3D), norms, normalization, and projections underpin geometry and optimization.
Category: Basics
Is a row vector different from a column vector?
They are different shapes but represent the same data; orientation matters for matrix multiplication and broadcasting rules in software libraries.
Category: Misunderstanding
How do you compute cosine similarity between vectors?
Cosine similarity is the dot product divided by the product of magnitudes. It measures orientation regardless of scale.
Category: Example
What is a unit vector and why use it?
A unit vector has norm 1. Normalization enables comparing directions and stabilizes numerical computations.
Category: Basics
How do vectors appear in gradient descent?
Gradients are vectors of partial derivatives. Updates subtract a scaled gradient vector from the parameter vector each iteration.
Category: Application
Are vectors always numeric?
Yes, but they can represent encoded categorical or textual data after transformation into numeric features.
Category: Misunderstanding