Calculates coefficients of the characteristic polynomial.
POLY(x)
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x |
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A series or matrix. A matrix where the eigenvalues are the roots of the returned polynomial coefficients or a series of the roots of the returned polynomial coefficients. |
A series, the polynomial coefficients in descending order.
W1: {{1, 2, 3},
{3, 4, 5},
{5, 6, 0}}
W2: poly(W1)
W3: polyroot(W2, 1)
W4: eig(W1)
W2 contains the series {1, -5, -47, -14}, the coefficients in descending order of the characteristic polynomial of the matrix in W1. The roots of this polynomial are the eigenvalues of the input matrix.
W3 == {9.894, -4.585, -0.309}
W4 == {9.894, -0.309, -4.585}
If the input is a series, the input represents the roots of the polynomial coefficients returned by POLY. For example, consider the polynomial:
poly({-2, -1}) == {1, 3, 2}
polyroot({1, 3, 2}, 1) == {-2, -1}
As indicated above, if the input is a matrix, POLY returns the coefficients of the characteristic polynomial in descending order.
If the input is a series, the input represents the roots of a polynomial and POLY returns the coefficients of this polynomial in descending order.