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How to convert polynomial to matrix? 
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#1
Apr1804, 11:31 AM

P: 1

Does anyone know how to convert a polynomial to a matrix. I have been told that it is possible to convert a fourth order polynomial to a 4x4 Matrix in Matlab but I have no clue how to go about it and how it is done. Any suggestions or even where to look would be GREATLY helpful!



#2
Apr1904, 09:50 PM

P: 3

Can you be more specific about what you are trying to do?
If you were to choose a basis for the space of fourth degree polynomials, like [tex] \{ 1,x,x^2,x^3,x^4 \} [/tex], then it is possible to represent a polynomial as an element of this vector space by a coefficient matrix. For example, [tex] 3x^42x^2+5 \mapsto \left[5,0,2,0,3 \right] [/tex]. This is not a 4x4 matrix like you are looking for, but it is a representation of the polynomial as a matrix. If you are more specific about what you are trying to do, maybe I can offer more insight, although I am not sure if what you want can be done. 


#3
Apr1111, 06:10 PM

P: 1

check this out for making a companion matrix for a given polynomial:
http://en.wikipedia.org/wiki/Companion_matrix The determinant of a companion matrix is a polynomial in λ, known as the characteristic polynomial. λs are the eigenvalues, they are also the solutions to the polynomial. This works well for polynomials of degree 4 or smaller since they can be solved by a finite sequence of arithmetic operations and radicals. hope this helps. 


#4
Apr2211, 06:25 AM

P: 7

How to convert polynomial to matrix?
use cayleyHamilton theorem from backwards,it will help...



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