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26.6 Miscellaneous Functions

Function File: poly (a)

If a is a square N-by-N matrix, poly (a) is the row vector of the coefficients of det (z * eye (N) - a), the characteristic polynomial of a. As an example we can use this to find the eigenvalues of a as the roots of poly (a).

roots(poly(eye(3)))
=> 1.00000 + 0.00000i
=> 1.00000 - 0.00000i
=> 1.00000 + 0.00000i

In real-life examples you should, however, use the eig function for computing eigenvalues.

If x is a vector, poly (x) is a vector of coefficients of the polynomial whose roots are the elements of x. That is, of c is a polynomial, then the elements of d = roots (poly (c)) are contained in c. The vectors c and d are, however, not equal due to sorting and numerical errors.

See also eig, roots

Function File: polyout (c, x)

Write formatted polynomial

c(x) = c(1) * x^n + ... + c(n) x + c(n+1)

and return it as a string or write it to the screen (if nargout is zero). x defaults to the string "s".

See also polyval, polyvalm, poly, roots, conv, deconv, residue, filter, polyderiv, and polyinteg

Function File: polyreduce (c)

Reduces a polynomial coefficient vector to a minimum number of terms by stripping off any leading zeros.

See also poly, roots, conv, deconv, residue, filter, polyval, polyvalm, polyderiv, polyinteg