2026-06-03T01:32:42Zhttps://riuma.uma.es/rest/oai/request

oai:riuma.uma.es:10630/328312026-02-03T11:13:46Zcom_10630_2254col_10630_37953

Best rank k approximation for binary forms. Ottaviani, Giorgio Tocino-Sánchez, Alicia Álgebra lineal Política de acceso abierto tomada de: https://www.sherpa.ac.uk/id/publication/28186 In the tensor space SymdR2 of binary forms we study the best rank k approximation problem. The critical points of the best rank 1 approximation problem are the eigenvectors and it is known that they span a hyperplane. We prove that the critical points of the best rank k approximation problem lie in the same hyperplane. As a consequence, every binary form may be written as linear combination of its critical rank 1 tensors, which extends the Spectral Theorem from quadratic forms to binary forms of any degree. In the same vein, also the best rank 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. 2024-09-23T09:31:47Z 2024-09-23T09:31:47Z 2017-09-11 journal article https://hdl.handle.net/10630/32831 10.1007/s13348-017-0206-6 eng open access Springer Nature