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3 Characteristic Polynomials We call the polynomial det(M − xI) the characteristic polynomial of matrix M.
000 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031 032 033 034 035 036 037 038 039 040 041 042 043 044 045 046 047 048 049 050 051 052 053 √ d for some First note that we just need to choose the degree of our Chebyshev polynomial q ≥ c ∗ log √ d is an integer constant c.
The standard way of solving the PEP (polynomial eigenvalue problem) P (λ)x = 0, where P (λ) is the matrix polynomial Ak λk + · · · + A1 λ + A0 and A0 , .
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Tangents, limits, and rules of differentiation for polynomial and trigonometric equations will be studied.
Remember that a polynomial generally expressed in the form anxn + an-1xn-1 + an-2xn-2 + … + a0 In our system will represent a polynomial by a curly brace enclosed list of coefficients:
It is possible to evaluate each of these as a polynomial through use of the elementary formulas for sums of consecutive powers.
the tittg R, whether there is a feedback gain matrix F over R iuch that with the LIhJEAR TIME-INVARIANT DISCRETE.TIME SYSTEMS 807 control (1.3), the resulting closed-loop characteristic polynomial det(zl* - A + BF) is equal to zn * an-Lzn-r + "' *arz * ao.