---
title: linear_operator (latest version)
description: API reference for qiskit_fermions.linalg.linear_operator in the latest version of qiskit-fermions
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit-fermions/linalg-linear-operator
---

# linear\_operator

`linear_operator(operator, norb, nelec)`

Returns a [`scipy.sparse.linalg.LinearOperator`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.LinearOperator.html#scipy.sparse.linalg.LinearOperator "(in SciPy v1.18.0)") for an operator on the `(norb, nelec)` FCI sector.

This is a thin, type-agnostic wrapper around the [`SupportsLinearOperator`](/docs/api/qiskit-fermions/protocols-supports-linear-operator "qiskit_fermions.protocols.SupportsLinearOperator") protocol method, mirroring the free-function style of [`ffsim.linear_operator()`](https://qiskit-community.github.io/ffsim/api/stubs/ffsim.linear_operator.html#ffsim.linear_operator "(in ffsim)").

**Parameters**

- **operator** ([*SupportsLinearOperator*](/docs/api/qiskit-fermions/protocols-supports-linear-operator "qiskit_fermions.protocols.linear_operator.SupportsLinearOperator")) – the operator to convert, implementing [`SupportsLinearOperator`](/docs/api/qiskit-fermions/protocols-supports-linear-operator "qiskit_fermions.protocols.SupportsLinearOperator").
- **norb** ([*int*](https://docs.python.org/3/library/functions.html#int)) – the number of spatial orbitals.
- **nelec** ([*int*](https://docs.python.org/3/library/functions.html#int)  *|*[*tuple*](https://docs.python.org/3/library/stdtypes.html#tuple)*\[*[*int*](https://docs.python.org/3/library/functions.html#int)*,* [*int*](https://docs.python.org/3/library/functions.html#int)*]*) – the electron count – an integer for a spinless sector, or an `(n_alpha, n_beta)` pair for a spinful one.

**Returns**

A [`scipy.sparse.linalg.LinearOperator`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.LinearOperator.html#scipy.sparse.linalg.LinearOperator "(in SciPy v1.18.0)") applying `operator` on the requested sector.

**Return type**

[*LinearOperator*](https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.LinearOperator.html#scipy.sparse.linalg.LinearOperator "(in SciPy v1.18.0)")