# **inner_product()**

## **Function Description**

`INNER_PRODUCT(vector1, vector2)` returns the negative dot product, `-(vector1 · vector2)`. Both vectors must have the same dimension.


## **Function Syntax**

```sql
SELECT inner_product(vector1, vector2) AS result FROM table_name;
```

## **Example**

```text
drop table if exists vec_table;
create table vec_table(a int, b vecf32(3), c vecf64(3));
insert into vec_table values(1, "[1,2,3]", "[4,5,6]");
mysql> select * from vec_table;
+-------+--------------------------+
| a | b | c |
+-------+--------------------------+
| 1 | [1, 2, 3] | [4, 5, 6] |
+-------+--------------------------+
1 row in set (0.00 sec)

mysql> select inner_product(b,"[1,2,3]") from vec_table;
+--------------------------------+
| inner_product(b, [1,2,3]) |
+--------------------------------+
|                       -14 |
+--------------------------------+
1 row in set (0.00 sec)
```

## **limit**

Two parameter vectors must have the same dimension.

## Sign and ordering

The current MOI backend returns the **negative dot product** for `INNER_PRODUCT(a, b)`: `-(a · b)`. The mathematical dot product of `[1,2,3]` and `[4,5,6]` is `32`, while the function returns `-32`. For `[1,2,3]` against itself, it returns `-14`.

Run this read-only query on the target instance to confirm the sign for its backend version:

```sql
SELECT INNER_PRODUCT('[1,2,3]', '[4,5,6]') AS negative_dot_product,
       INNER_PRODUCT('[1,2,3]', '[1,2,3]') AS self_negative_dot_product;
```

Under the negative-dot-product convention, the results are `-32` and `-14`. For similarity retrieval, use `ORDER BY INNER_PRODUCT(vector_column, query_vector) ASC`: a larger mathematical dot product produces a smaller negative dot product. Use `-INNER_PRODUCT(a, b)` when you need the mathematical dot product.

Run the constant query again after changing backend versions before choosing the sort direction. If it returns positive values, that instance uses a different sign convention and the `ASC` ordering above does not apply directly.