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We study the structured distance to singularity for a given regular matrixpencil $A+sE$, where $(A,E)\in \mathbb S \subseteq (\mathbb C^{n,n})^2$. Thisincludes Hermitian, skew-Hermitian, $*$-even, $*$-odd, $*$-palindromic,T-palindromic, and dissipative Hamiltonian pencils. We present a purely linearalgebra-based approach to derive explicit computable formulas for the distanceto the nearest structured pencil $(A-\Delta_A)+s(E-\Delta_E)$ such that$A-\Delta_A$ and $E-\Delta_E$ have a common null vector. We then obtain afamily of computable lower bounds for the unstructured and structured distancesto singularity. Numerical experiments suggest that in many cases, there is asignificant difference between structured and unstructured distances.  This approach extends to structured matrix polynomials with higher degrees.

Estimation to structured distances to singularity for matrix pencils with symmetry structures: A linear algebra-based approach