# 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.

#### References

SHOWING 1-3 OF 3 REFERENCES

Successful Pressing Sequences for a Bicolored Graph and Binary Matrices

- Mathematics
- 2015

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 computational… Expand

Uniquely pressable graphs: Characterization, enumeration, and recognition

- Mathematics, Computer Science
- Adv. Appl. Math.
- 2019

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