RT Journal Article
T1 Best rank k approximation for binary forms.
A1 Ottaviani, Giorgio
A1 Tocino-Sánchez, Alicia
K1 Álgebra lineal
AB In the tensor space SymdR2 of binary forms we study the best rank k approximationproblem. The critical points of the best rank 1 approximation problem are the eigenvectorsand it is known that they span a hyperplane. We prove that the critical points of the best rankk approximation problem lie in the same hyperplane. As a consequence, every binary formmay be written as linear combination of its critical rank 1 tensors, which extends the SpectralTheorem from quadratic forms to binary forms of any degree. In the same vein, also the bestrank k approximation may be written as a linear combination of the critical rank 1 tensors,which extends the Eckart–Young theorem from matrices to binary forms.
PB Springer Nature
YR 2017
FD 2017-09-11
LK https://hdl.handle.net/10630/32831
UL https://hdl.handle.net/10630/32831
LA eng
NO Política de acceso abierto tomada de: https://www.sherpa.ac.uk/id/publication/28186
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 20 ene 2026