Mathematics for ML

Dot Product, explained

The dot product combines two vectors into a single number that reflects their alignment and magnitude.
Back to Glossary

Part of the Semantic Notion technical glossary.

Short Definition

The dot product combines two vectors into a single number that reflects their alignment and magnitude.

Intuition

If two vectors point in similar directions, their dot product is larger.

Technical Definition

The dot product is the sum of elementwise products between two equal-length vectors.

Example

Attention computes query-key similarity using dot products.

Common Misunderstandings

Dot product depends on vector magnitude as well as direction.
Cosine similarity removes magnitude by normalizing vectors.

Same Category

More from Mathematics for ML

Cosine SimilarityCosine similarity measures how similar two vectors are by comparing their direction rather than their magnitude.Cross-EntropyCross-entropy measures how well one probability distribution matches another, often a model prediction against a target label.EigenvalueAn eigenvalue is the scaling factor applied to an eigenvector by a linear transformation.EigenvectorAn eigenvector is a nonzero vector whose direction stays the same under a linear transformation.EntropyEntropy measures uncertainty or information content in a probability distribution.Euclidean DistanceEuclidean distance is the straight-line distance between two points in a vector space.

Related Reading

Essays that use this concept

Vector Search and RetrievalCosine Similarity vs Euclidean Distance vs Dot Product

Start here

Need the broader concept map?

Return to the glossary index to move from this definition into adjacent AI, ML, mathematics, and computer science terms.

Browse Glossary