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> Reference for vector functions

# Vector functions

## Vector functions

Vector functions operate on arrays of numeric data to perform mathematical calculations on numeric vectors. These functions calculate distances and similarities between vectors, as well as perform arithmetic operations.

```sql theme={"theme":{"light":"github-light","dark":"github-dark"}}
SELECT VECTOR_EUCLIDEAN_DISTANCE([1.0, 2.0, 3.0], [4.0, 5.0, 6.0]) AS distance;
```

Vector functions require input arrays to have the same number of elements and contain numeric data types. Distance and similarity functions return `DOUBLE` precision values, while arithmetic operations return arrays with elements that follow Firebolt's type conversion rules.

Vector distance functions measure the mathematical distance or similarity between two numeric arrays. Common applications include:

* **Similarity analysis** - Finding similar items based on their feature vectors
* **Machine learning** - Computing distances for clustering, classification, and recommendation algorithms
* **Spatial calculations** - Measuring distances between points in multi-dimensional space
* **Data analysis** - Comparing numeric datasets and identifying patterns