Previous: Polynomial Interpolation, Up: Polynomial Manipulations [Contents][Index]
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.
For example, the following code finds the eigenvalues of A which are
the roots of poly (A)
.
roots (poly (eye (3))) ⇒ 1.00001 + 0.00001i 1.00001 - 0.00001i 0.99999 + 0.00000i
In fact, all three eigenvalues are exactly 1 which emphasizes that for
numerical performance the eig
function should be used to compute
eigenvalues.
If x is a vector, poly (x)
is a vector of the
coefficients of the polynomial whose roots are the elements of x.
That is, if c is a polynomial, then the elements of
d = roots (poly (c))
are contained in c. The
vectors c and d are not identical, however, due to sorting and
numerical errors.
Display a formatted version of the polynomial c.
The formatted polynomial
c(x) = c(1) * x^n + … + c(n) x + c(n+1)
is returned as a string or written to the screen if nargout
is zero.
The second argument x specifies the variable name to use for each term
and defaults to the string "s"
.
See also: polyreduce.
Reduce a polynomial coefficient vector to a minimum number of terms by stripping off any leading zeros.
See also: polyout.
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