In an ageing society, families may have an important role in the caretaking and well-being of the elderly. Demographic changes have an impact on the size and structure of families; one aspect is how intergenerational support is distributed when there is a need for support to both older and younger generations at the same time. Another vital aspect of the provision of care for the elderly is geo...

For a matrix polynomial P (λ) and a given complex number μ, we introduce a (spectral norm) distance from P (λ) to the matrix polynomials that have μ as an eigenvalue of geometric multiplicity at least κ, and a distance from P (λ) to the matrix polynomials that have μ as a multiple eigenvalue. Then we compute the first distance and obtain bounds for the second one, constructing associated pertur...