Upper Hessenberg Bohemian matrices with entries in {-1,0,1} yield characteristic polynomials of maximal height that grow exponentially with matrix order, with explicit polynomials, bounds, an asymptotic conjecture, and theorems on normal and stable matrices identified.
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Upper Hessenberg and Toeplitz Bohemians
Upper Hessenberg Bohemian matrices with entries in {-1,0,1} yield characteristic polynomials of maximal height that grow exponentially with matrix order, with explicit polynomials, bounds, an asymptotic conjecture, and theorems on normal and stable matrices identified.