Rank-reducibility of a Symmetric Matrix and Sampling Theory

@inproceedings{TRACE1982RankreducibilityOA,
  title={Rank-reducibility of a Symmetric Matrix and Sampling Theory},
  author={O F M I N I M U M TRACE},
  year={1982}
}
  • O F M I N I M U M TRACE
  • Published 1982
One of the intriguing questions of factor analysis is the extent to which one can reduce the rank of a symmetric matrix by only changing its diagonal entries. We show in this paper that the set of matrices, which can be reduced to rank r, has positive (Lebesgue) measure if and only if r is greater or equal to the Ledermann bound. In other words the Ledermann bound is shown to be almost surely the greatest lower bound to a reduced rank of the sample covariance matrix. Afterwards an asymptotic… CONTINUE READING

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