Corpus ID: 237490280

On the Number of Cholesky Roots of the Zero Matrix over F2

@inproceedings{Whitlatch2021OnTN,
  title={On the Number of Cholesky Roots of the Zero Matrix over F2},
  author={Hays Whitlatch},
  year={2021}
}
A square, upper-triangular matrix U is a Cholesky root of a matrix M provided U ∗ U = M , where ∗ represents the conjugate transpose. Over finite fields, as well as over the reals, it suffices for U T U = M . In this paper, we investigate the number of such factorizations over the finite field with two elements, F2, and prove the existence of a rank-preserving bijection between the number of Cholesky roots of the zero matrix and the upper-triangular square roots the zero matrix. 

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