arXiv subjects

Michal Krizek

Publications and source records attributed to Michal Krizek.

2 recordsLinked to original sources

arXiv2026

Two-sided bounds for dihedral angle sums of path and 4-ball tetrahedra

A tetrahedron is called a path tetrahedron, if it has three mutually orthogonal edges that do not intersect at a single point. A tetrahedron is called a 4-ball tetrahedron, if there exists a sphere tangent to all its edges. We derive two-sided tight bounds for dihedral angle sums of such tetrahedra. In particular, we prove that this sum lies in the interval (2{\pi}, 2.5{\pi}) for path tetrahedra and in [6 arccos 1/3, 3{\pi}) for 4-ball tetrahedra. Also some of their useful properties are presented.

math.MG↗

arXiv2016

Factorization of CP-rank-3 completely positive matrices

A symmetric positive semi-definite matrix A is called completely positive if there exists a matrix B with nonnegative entries such that A=BB^T. If B is such a matrix with a minimal number p of columns, then p is called the cp-rank of A. In this paper we develop a finite and exact algorithm to factorize any matrix A of cp-rank 3. Failure of this algorithm implies that A does not have cp-rank 3. Our motivation stems from the question if there exist three nonnegative polynomials of degree at most four that vanish at the boundary of an interval and are orthonormal with respect to a certain inner product.

math.RA↗