Documentation

This is machine translation

Translated by Microsoft
Mouse over text to see original. Click the button below to return to the English verison of the page.

我们为许可用户提供了部分翻译好的中文文档。您只需登录便可查阅这些文档

polyvalm

Matrix polynomial evaluation

Syntax

Description

example

Y = polyvalm(p,X) returns the evaluation of polynomial p in a matrix sense. This evaluation is the same as substituting matrix X in the polynomial, p.

Examples

collapse all

Find the characteristic polynomial of a Pascal Matrix of order 4.

X =  pascal(4)
p = poly(X)
X =

     1     1     1     1
     1     2     3     4
     1     3     6    10
     1     4    10    20


p =

    1.0000  -29.0000   72.0000  -29.0000    1.0000

The characteristic polynomial is

$$p(x) = x^4 - 29x^3 + 72x^2  -29x + 1$$

Pascal matrices have the property that the vector of coefficients of the characteristic polynomial is the same forward and backward (palindromic).

Substitute the matrix, X, into the characteristic equation, p. The result is very close to being a zero matrix. This example is an instance of the Cayley-Hamilton theorem, where a matrix satisfies its own characteristic equation.

Y = polyvalm(p,X)
Y =

   1.0e-10 *

   -0.0013   -0.0063   -0.0104   -0.0241
   -0.0048   -0.0217   -0.0358   -0.0795
   -0.0114   -0.0510   -0.0818   -0.1805
   -0.0228   -0.0970   -0.1553   -0.3396

Input Arguments

collapse all

Polynomial coefficients, specified as a vector. For example, the vector [1 0 1] represents the polynomial x2+1, and the vector [3.13 -2.21 5.99] represents the polynomial 3.13x22.21x+5.99.

For more information, see Create and Evaluate Polynomials.

Data Types: single | double
Complex Number Support: Yes

Input matrix, specified as a square matrix.

Data Types: single | double
Complex Number Support: Yes

Output Arguments

collapse all

Output polynomial coefficients, returned as a row vector.

See Also

|

Introduced before R2006a


Was this topic helpful?