Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the problems of completing a low-rank positive semidefinite square matrix M or a low-rank rectangular matrix N from a given subset of their entries.  study the local and global uniqueness of such completions by analyzing the structure of the graphs determined by the positions of the known entries of M or N. show that, in the generic setting, the unique completability testing of rectangular matrices is a special case of the unique completability testing of positive semidefinite matrices.  prove that a generic partially filled semidefinite n × n matrix is globally uniquely rank d completable if any principal minor of size n - 1 is locally uniquely rank d completable. These results are based on new geometric observations that extend similar results of the theory of rigid frameworks.  also give an example showing that global completability is not a generic property in R 2 . provide sufficient conditions for local and global unique completability of a partially filled matrix in terms of either the minimum number of known entries per row or the total number of known entries.
['Bill Jackson', 'Tibor Jordán', 'Shin ichi Tanigawa']
I am writing a research paper on a idea Unique low rank completability of partially filled matrices
[{"from": "human", "value": "I am writing a research paper on a idea Unique low rank completability of partially filled matrices"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the problems of completing a low-rank positive semidefinite square matrix M or a low-rank rectangular matrix N from a given subset of their entries.  study the local and global uniqueness of such completions by analyzing the structure of the graphs determined by the positions of the known entries of M or N. show that, in the generic setting, the unique completability testing of rectangular matrices is a special case of the unique completability testing of positive semidefinite matrices.  prove that a generic partially filled semidefinite n \u00d7 n matrix is globally uniquely rank d completable if any principal minor of size n - 1 is locally uniquely rank d completable. These results are based on new geometric observations that extend similar results of the theory of rigid frameworks.  also give an example showing that global completability is not a generic property in R 2 . provide sufficient conditions for local and global unique completability of a partially filled matrix in terms of either the minimum number of known entries per row or the total number of known entries."}]