Corpus ID: 237490280

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

  title={On the Number of Cholesky Roots of the Zero Matrix over F2},
  author={Hays Whitlatch},
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. 


Successful Pressing Sequences for a Bicolored Graph and Binary Matrices
We apply matrix theory over $\mathbb{F}_2$ to understand the nature of so-called "successful pressing sequences" of black-and-white vertex-colored graphs. These sequences arise in computationalExpand
Uniquely pressable graphs: Characterization, enumeration, and recognition
This work addresses the question of when a graph has precisely one such pressing sequence, thus answering an question from Cooper and Davis (2015), and characterize uniquely pressable graphs, count the number of them on a given number of vertices, and provide a polynomial time recognition algorithm. Expand
The number of solutions of x2= 0 in triangular matrices over gf (q)
  • Electron. J. Comb,
  • 1996