Singular value decomposition

URI: https://gptkb.org/entity/Singular_value_decomposition
GPTKB entity
Statements (36)
Predicate Object
gptkbp:instanceOf matrix decomposition
gptkbp:abbreviation gptkb:SVD
gptkbp:appliesTo complex matrices
real matrices
gptkbp:category gptkb:mathematics
numerical linear algebra
gptkbp:decomposes gptkb:group_of_people
gptkbp:decompositionForm A = UΣV*
gptkbp:field linear algebra
https://www.w3.org/2000/01/rdf-schema#label Singular value decomposition
gptkbp:introduced gptkb:Camille_Jordan
gptkb:Erhard_Schmidt
gptkb:Carl_Eckart
gptkb:Eugenio_Beltrami
gptkb:Gale_Young
gptkbp:introducedIn 1873
1907
1936
gptkbp:property U and V are orthogonal (real case)
U and V are unitary (complex case)
singular values are non-negative
singular values are unique
gptkbp:relatedTo gptkb:spectral_theorem
eigenvalue decomposition
gptkbp:U unitary matrix
gptkbp:usedFor gptkb:principal_component_analysis
gptkb:signal_processing
data compression
solving linear systems
matrix approximation
latent semantic analysis
pseudoinverse computation
gptkbp:V* conjugate transpose of unitary matrix
gptkbp:Σ diagonal matrix
gptkbp:bfsParent gptkb:Eigenvalue_decomposition
gptkbp:bfsLayer 6