VECTOR_NORM

Calculates the L2 norm (Euclidean norm) of a vector, which represents the length or magnitude of the vector.

Syntax

VECTOR_NORM(vector)

Arguments

• vector: Input vector (VECTOR Data Type)

Returns

Returns a FLOAT value representing the L2 norm (magnitude) of the vector.

Description

The VECTOR_NORM function calculates the L2 norm (also known as Euclidean norm) of a vector, which represents its length or magnitude in Euclidean space. The function:

1. Squares each element of the vector
2. Sums all the squared values
3. Returns the square root of the sum

The mathematical formula implemented is:

vector_norm(v) = √(Σ(vᵢ²))

Where vᵢ are the elements of the input vector.

The vector norm is fundamental in:

• Normalizing vectors to unit length
• Measuring vector magnitude in machine learning
• Computing distances and similarities
• Feature scaling and preprocessing
• Physics calculations involving magnitude

Examples

-- Calculate vector magnitude (length)
SELECT
    VECTOR_NORM([3,4]::VECTOR(2)) AS norm_2d,
    VECTOR_NORM([1,2,3]::VECTOR(3)) AS norm_3d,
    VECTOR_NORM([0,0,0]::VECTOR(3)) AS zero_vector;

Result:

┌─────────┬───────────┬─────────────┐
│ norm_2d │  norm_3d  │ zero_vector │
├─────────┼───────────┼─────────────┤
│     5.0 │ 3.7416575 │         0.0 │
└─────────┴───────────┴─────────────┘