Does a Singular Symmetric Interval Matrix Contain a Symmetric Singular Matrix?

0505752 - ÚI 2020 CZ eng V - Research Report
Rohn, Jiří
Does a Singular Symmetric Interval Matrix Contain a Symmetric Singular Matrix?.
Prague: ICS CAS, 2019. 7 s. Technical Report, V-1268.
Institutional support: RVO:67985807
Keywords : symmetric interval matrix * singularity * positive semide niteness
OECD category: Pure mathematics

We consider the conjecture formulated in the title concerning existence of a symmetric singular matrix in a singular symmetric interval matrix. We show by means of a counterexample that it is generally not valid, and we prove that it becomes true under an additional assumption of positive semide niteness of the midpoint matrix. The proof is constructive.
Permanent Link: http://hdl.handle.net/11104/0297149