7. Singular value decomposition

Singular value decomposition (SVD) has important applications in a wide variety of scientific fields. This decomposition can be seen as a generalization of the spectral decomposition of a Hermitian matrix, which is a decomposition of A into a product of the form A = U DU ^H where U is unitary and D diagonal. However, the SVD decomposition exists for any matrix, even in the case of rectangular matrices.

Theorem 13

For any matrix $A \in ℝ^{m \times n}$ , there exist orthogonal matrices

You do not have access to this resource.

Exclusive to subscribers. 97% yet to be discovered!

You do not have access to this resource. Click here to request your free trial access!

Already subscribed? Log in!

Ongoing reading
Singular value decomposition

Previous
page Generalized eigenvalue problem

Conclusion

Article included in this offer

"Mathematics"

( 165 articles )

Complete knowledge base

Updated and enriched with articles validated by our scientific committees

Services

A set of exclusive tools to complement the resources

View offer details

Bibliography

References

(1) - ANDERSON (E.), BAI (Z.), BISCHOF (C.), BLACKFORD (L.S.), DEMMEL (J.), DONGARRA (J.J.), DU CROZ (J.), HAMMARLING (S.), GREENBAUM (A.), McKENNEY (A.), SORENSEN (D.) - LAPACK Users' guide (3e éd.). - Society for Industrial and Applied Mathematics, Philadelphia, PA, USA (1999).

You do not have access to this resource.

Exclusive to subscribers. 97% yet to be discovered!

You do not have access to this resource. Click here to request your free trial access!

Already subscribed? Log in!