# inner_product

Graph.inner_product(x, y, *, name=None)

Calculate the inner product of two vectors.

The vectors must have the same last dimension and broadcastable shapes.

### Parameters

• x (np.ndarray or Tensor) – The left multiplicand. It must be a vector of shape (..., D).
• y (np.ndarray or Tensor) – The right multiplicand. It must be a vector of shape (..., D).
• name (str or None , optional) – The name of the node.

### Returns

The inner product of two vectors of shape (...).

### Return type

Tensor

Graph.density_matrix_expectation_value : Expectation value of an operator with respect to a density matrix.

Graph.einsum : Tensor contraction via Einstein summation convention.

Graph.expectation_value : Expectation value of an operator with respect to a pure state.

Graph.outer_product : Outer product of two vectors.

Graph.trace : Trace of an object.

## Notes

The inner product or dot product of two complex vectors $\mathbf{x}$ and $\mathbf{y}$ is defined as

$\langle \mathbf{x} \vert \mathbf{y} \rangle = \sum_i x^\ast_{i} y_{i} .$

For more information about the inner product, see dot product on Wikipedia.

## Examples

>>> graph.inner_product(np.array([1j, 1j]), np.array([1j, 1j]), name="inner")
<Tensor: name="inner", operation_name="inner_product", shape=()>
>>> result = bo.execute_graph(graph=graph, output_node_names="inner")
>>> result["output"]["inner"]["value"]
2.+0.j
>>> graph.inner_product(np.ones((3,1,4), np.ones(2,4), name="inner2")
<Tensor: name="inner2", operation_name="inner_product", shape=(3, 2)>
>>> result = bo.execute_graph(graph=graph, output_node_names="inner2")
>>> result["output"]["inner2"]["value"]
array([[4, 4], [4, 4], [4, 4]])