polyvalm
Matrix polynomial evaluation
Syntax
Description
Examples
Matrix Evaluation of Characteristic Polynomial
Find the characteristic polynomial of a Pascal Matrix of order 4.
X = pascal(4)
X = 4×4
1 1 1 1
1 2 3 4
1 3 6 10
1 4 10 20
p = poly(X)
p = 1×5
1.0000 -29.0000 72.0000 -29.0000 1.0000
The characteristic polynomial is
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 = 4×4
10-10 ×
-0.0014 -0.0064 -0.0105 -0.0242
-0.0049 -0.0220 -0.0362 -0.0801
-0.0116 -0.0514 -0.0827 -0.1819
-0.0230 -0.0976 -0.1567 -0.3424
Input Arguments
p
— Polynomial coefficients
vector
Polynomial coefficients, specified as a vector. For example,
the vector [1 0 1]
represents the polynomial ,
and the vector [3.13 -2.21 5.99]
represents the
polynomial .
For more information, see Create and Evaluate Polynomials.
Data Types: single
| double
Complex Number Support: Yes
X
— Input matrix
square matrix
Input matrix, specified as a square matrix.
Data Types: single
| double
Complex Number Support: Yes
Output Arguments
Y
— Output polynomial coefficients
row vector
Output polynomial coefficients, returned as a row vector.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Thread-Based Environment
Run code in the background using MATLAB® backgroundPool
or accelerate code with Parallel Computing Toolbox™ ThreadPool
.
This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.
GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
The polyvalm
function
fully supports GPU arrays. To run the function on a GPU, specify the input data as a gpuArray
(Parallel Computing Toolbox). For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.
This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).
Version History
Introduced before R2006a
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