Calculation of eigenvalues : Singular value decomposition

Singular value decomposition
Calculation of eigenvalues

Authors : Bernard PHILIPPE, Yousef SAAD

Publication date: October 10, 2008 | Lire en français

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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

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Singular value decomposition

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Conclusion

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).

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Singular value decomposition Calculation of eigenvalues

7. Singular value decomposition

Bibliography

References

Singular value decomposition
Calculation of eigenvalues