VECTOR_INNER_PRODUCT

Returns the inner product, also known as the dot or scalar product, between two vectors. The inner product measures how closely two vectors align with each other, both in magnitude and the cosine of the angle between them. It is calculated by multiplying the corresponding elements of the vectors and then summing the results. If the vectors have similar directions and large magnitudes, the inner product has a large positive value. If they are orthogonal, the inner product is zero, regardless of magnitude. If they point in roughly opposite directions, and at least one has a small magnitude, the inner product is small and negative. Alias: inner_product (aligned with pgvector for compatibility)

Syntax

VECTOR_INNER_PRODUCT(<array>, <array>)

Parameters

Parameter	Description	Supported input types
`<array>`	The first array used in the inner product calculation.	Any array of numeric data types.
`<array>`	The second array used in the inner product calculation.	Any array of numeric data types.

Notes

Both input array arguments must have the same number of elements.

Return Type

DOUBLE

Examples

Example The following code returns the inner product of two vectors that have similar directions and magnitudes:

SELECT VECTOR_INNER_PRODUCT([1, 2], [3, 4]) AS product;

product double
11

Rows: 1Execution time: 6.29ms

Example The following code returns the inner product of two vectors that are orthogonal to each other:

SELECT VECTOR_INNER_PRODUCT([3, 4], [-4, 3]) AS product;

product double
0

Rows: 1Execution time: 5.46ms

Example The following code returns the inner product of two vectors that are pointing in very different directions that are not orthogonal:

SELECT VECTOR_INNER_PRODUCT([3, 4], [4, -2]) AS product;

product double
4

Rows: 1Execution time: 5.81ms

VECTOR_EUCLIDEAN_DISTANCE

VECTOR_MANHATTAN_DISTANCE

⌘I

Overview

Performance and Observability

Security

Self-Managed

Managed service

Guides

SQL reference

Release notes

API reference

Legal

VECTOR_INNER_PRODUCT