How to solve the pole of polynomial with matrix coefficient

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SUMMARY

This discussion addresses the challenge of finding poles of polynomials with matrix coefficients, specifically in the form "A*s^2 + C = 0", where A and C are 3x3 constant matrices. The user initially employs the "roots" function for scalar polynomials but seeks a simpler command for matrix polynomials. The recommended solution is to utilize Gaussian elimination, which effectively handles such matrix equations.

PREREQUISITES
  • Understanding of polynomial equations and their roots
  • Familiarity with matrix algebra and operations
  • Knowledge of MATLAB or similar computational tools
  • Basic understanding of Gaussian elimination technique
NEXT STEPS
  • Research the implementation of Gaussian elimination in MATLAB
  • Explore matrix polynomial equations and their properties
  • Learn about MATLAB's "sym" and "solve" functions for symbolic computation
  • Investigate numerical methods for solving matrix equations
USEFUL FOR

Mathematicians, engineers, and computer scientists dealing with control systems, signal processing, or any field requiring the analysis of polynomial equations with matrix coefficients.

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Hi! This is my first post here. If I make any mistake, please tell me.

I have a question: if I want to find a pole of a polynomial, ex: " a*s^2+b*s+c ", a,b,and c are constant given. I just use simple command: roots([a, b,c]), I can get the answer.
However, if now I meet a situation is " A*s^2+C=0 ", A and C are all 3*3 constant matrices, I used the " sym and solve " to find the equation. It's OK. However, except this method, is there any simple command, just like " roots " to solve the polynomial with matrix coefficient?

Thanks!
 
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