> ## Documentation Index
> Fetch the complete documentation index at: https://docs.risingwave.com/llms.txt
> Use this file to discover all available pages before exploring further.

# Vector data type

> Introduces the vector data type along with the functions and operators available for working with vectors

RisingWave supports a dedicated vector(n) data type to represent fixed-length numerical vectors, similar to the [`pgvector`](https://github.com/pgvector/pgvector) extension in PostgreSQL. Vectors are commonly used to store embeddings and other high-dimensional feature data.

## Define a vector type

```sql theme={null}
vector(n)
```

`n` is a positive integer specifying the number of dimensions (elements) in the vector. All elements are stored as real (float32) values, and they must be finite numbers,`NULL`, `NaN`, `inf`, and `-inf` are not allowed. Vectors are represented in SQL using a bracketed, comma-separated list format such as `[1.0, 2.0, 3.0]`.

## Examples

```sql theme={null}
-- Create a table with vector columns
CREATE TABLE embeddings (
    id INT PRIMARY KEY,
    text_content VARCHAR,
    embedding vector(128),  -- 128-dimensional vector
    features vector(3)      -- 3-dimensional vector
);

-- Insert vector data
INSERT INTO embeddings VALUES 
(1, 'Sample text', '[0.1, 0.2, 0.3, ...]', '[1.0, 2.0, 3.0]'),
(2, 'Another text', '[0.4, 0.5, 0.6, ...]', '[4.0, 5.0, 6.0]');
```

## Type casts

Vectors can be converted between other types using casts:

| From                                                    | To          | Cast type |
| :------------------------------------------------------ | :---------- | :-------- |
| `vector(n)`                                             | `varchar`   | assign    |
| `varchar`                                               | `vector(n)` | explicit  |
| `vector(n)`                                             | `real[]`    | implicit  |
| `int[]` / `numeric[]` / `real[]` / `double precision[]` | `vector(n)` | assign    |

## Distance functions

RisingWave provides built-in operators and functions for measuring distance and similarity between vectors.

| Operator / Function                                                                                       | Note                   |
| :-------------------------------------------------------------------------------------------------------- | :--------------------- |
| `vector(n) <-> vector(n) → double precision` / `l2_distance(vector(n), vector(n)) → double precision`     |                        |
| `vector(n) <=> vector(n) → double precision` / `cosine_distance(vector(n), vector(n)) → double precision` |                        |
| `vector(n) <+> vector(n) → double precision` / `l1_distance(vector(n), vector(n)) → double precision`     |                        |
| `vector(n) <#> vector(n) → double precision`                                                              | Negative inner product |
| `inner_product(vector(n), vector(n)) → double precision`                                                  |                        |

## Other vector operators

In addition to distance functions, RisingWave supports element-wise operations and vector transformations:

| Operator / Function                         | Description                   |
| :------------------------------------------ | :---------------------------- |
| `vector(n) + vector(n) → vector(n)`         | Element-wise addition         |
| `vector(n) - vector(n) → vector(n)`         | Element-wise subtraction      |
| `vector(n) * vector(n) → vector(n)`         | Element-wise multiplication   |
| `vector(m) \|\| vector(n) → vector(m+n)`    | Concatenate two vectors       |
| `vector_norm(vector(n)) → double precision` | Euclidean norm                |
| `l2_normalize(vector(n)) → vector(n)`       | Normalize with Euclidean norm |