poly

Polynomial Coefficients

Usage

poly(a)

• a should be a vector or a square matrix of numeric values (non-characters).
• If a is a vector, it returns cofficients of the polynomial with roots given by a. The first and the last coefficients correspond to the highest and the zeroth order terms, respectively.
• If a is a square matrix, it returns coefficients of the characteristic polynomial of a. For $I$ being an identity matrix, the characteristic polynomial is given by

• a should not contain inf nor nan values.
• If a is empty, it returns 1.

Examples

• Plotting the polynomial having roots [3 4 5].

Input

r = [3 4 5];
p = poly(r);
x = linspace(2.8,5.5);
plot(x,polyval(p,x))

Output

p =
 1.000  -12.00   47.00  -60.00

Plot is generated.

• The following example obtains coefficients of the characteristic polynomial of $\begin{bmatrix}1&2\\3&4\end{bmatrix}$, i.e.,

Input

A = [1 2;3 4];
p = poly(A)

Output

p =
 1.000  -5.000  -2.000