This paper quantifies the net impact (direct and indirect effects) of the pandemic on the United States population in 2020 using three metrics: excess deaths, life expectancy, and total years of life lost. The findings indicate there were 375,235 excess deaths, with 83% attributable to direct, and 17% attributable to indirect effects of COVID-19. The decrease in life expectancy was 1.67 years, translating to a reversion of 14 years in historical life expectancy gains. Total years of life lost in 2020 was 7,362,555 across the USA (73% directly attributable, 27% indirectly attributable to COVID-19), with considerable heterogeneity at the individual state level.

We look at Bohemians, specifically those with population {−1, 0, +1} and sometimes {0,1,i, − 1, − i}. More, we specialize the matrices to be upper Hessenberg Bohemian. From there, focusing on only those matrices whose characteristic polynomials have maximal height allows us to explicitly identify these polynomials and give useful bounds on their height, and conjecture an accurate asymptotic formula. The lower bound for the maximal characteristic height is exponential in the order of the matrix; in contrast, the height of the matrices remains constant. We give theorems about the numbers of normal matrices and the numbers of stable matrices in these families.

We show how to construct linearizations of matrix polynomials za(z)d 0 + c 0 ,and za(z)d 0 b(z)+c 0 from linearizations of the component parts, a(z) and b(z). This allows the extension to matrix polynomials of a new companion matrix construction. Keywords: companion matrices, linearization, matrix polynomials, block upper Hessenberg 2010 MSC: 65F99, 15A22 IntroductionMany applications require the computation or approximation of polynomial eigenvalues, that is, those z ∈ C for which the matrix polynomial P(z) (of degree at most s) ∈ C[z] r×r is singular. In other words, we search for z such that det P(z) = 0. If s = 1, that is P(z) = zB−A, where A, B ∈ C N ×N , where N = r, is degree 1 in z, i.e. linear, then this is "just" the generalized eigenvalue problem, which can be reliably solved numerically on many platforms using software developed over many decades by the efforts of many people. We do