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

# Linear Algebra Utilities

This module provides various linear algebra utilities.

|                                                                                                                                                                                                                                            |                                                                                                                                                                                                                                                           |
| ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| [`apply_unitary`](/docs/api/qiskit-fermions/linalg-apply-unitary#qiskit_fermions.linalg.apply_unitary "qiskit_fermions.linalg.apply_unitary")(vec, operator, norb, nelec\[, copy])                                                         | Applies a unitary transformation to a state vector.                                                                                                                                                                                                       |
| [`givens_decomposition`](/docs/api/qiskit-fermions/linalg-givens-decomposition#qiskit_fermions.linalg.givens_decomposition "qiskit_fermions.linalg.givens_decomposition")(unitary)                                                         | Decomposes a unitary matrix into Givens rotations and diagonal phases.                                                                                                                                                                                    |
| [`givens_decomposition_slater`](/docs/api/qiskit-fermions/linalg-givens-decomposition-slater#qiskit_fermions.linalg.givens_decomposition_slater "qiskit_fermions.linalg.givens_decomposition_slater")(orbital\_coeffs)                     | Decomposes the occupied orbitals of a Slater determinant into Givens rotations.                                                                                                                                                                           |
| [`double_factorized_2body`](/docs/api/qiskit-fermions/linalg-double-factorized-2-body#qiskit_fermions.linalg.double_factorized_2body "qiskit_fermions.linalg.double_factorized_2body")(two\_body\_tensor, tol)                             | Double-factorized decomposition of a real two-body tensor.                                                                                                                                                                                                |
| [`double_factorized_t2`](/docs/api/qiskit-fermions/linalg-double-factorized-t-2#qiskit_fermions.linalg.double_factorized_t2 "qiskit_fermions.linalg.double_factorized_t2")(t2\_amplitudes, tol\[, ...])                                    | Double-factorized decomposition of spin-restricted $t_2$ amplitudes.                                                                                                                                                                                      |
| [`linear_operator`](/docs/api/qiskit-fermions/linalg-linear-operator#qiskit_fermions.linalg.linear_operator "qiskit_fermions.linalg.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. |
| [`reconstruct_t2`](/docs/api/qiskit-fermions/linalg-reconstruct-t-2#qiskit_fermions.linalg.reconstruct_t2 "qiskit_fermions.linalg.reconstruct_t2")(terms, nocc)                                                                            | Reconstructs spin-restricted $t_2$ amplitudes from a double-factorized decomposition.                                                                                                                                                                     |
| [`double_factorized_t2_alpha_beta`](/docs/api/qiskit-fermions/linalg-double-factorized-t-2-alpha-beta#qiskit_fermions.linalg.double_factorized_t2_alpha_beta "qiskit_fermions.linalg.double_factorized_t2_alpha_beta")(...\[, max\_terms]) | Double-factorized decomposition of alpha-beta (spin-unrestricted) $t_2$ amplitudes.                                                                                                                                                                       |
| [`reconstruct_t2_alpha_beta`](/docs/api/qiskit-fermions/linalg-reconstruct-t-2-alpha-beta#qiskit_fermions.linalg.reconstruct_t2_alpha_beta "qiskit_fermions.linalg.reconstruct_t2_alpha_beta")(terms, norb, ...)                           | Reconstructs alpha-beta $t_2$ amplitudes from a double-factorized decomposition.                                                                                                                                                                          |