what if the some rows of matrix M is zeros

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Chandan 2023-4-24

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评论： Chandan 2023-12-11

In fluid mechnics problems, we get quadratic eigenvalue problem . But most of the element of the co-effiencient matrix of lamda^2 are zeros. When i used polyeig function i am getting some of the eigenvalue as infinity? how to interpret the results

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Matt J 2023-4-24

Please Demonstrate what you are seeing for us.

Chandan 2023-4-24

编辑：Torsten 2023-4-24

在 MATLAB Online 中打开

polyeig function solve polynomial eigenvalue problem. Such as an example (Mλ^2+Cλ+K)x=0, where λ is eigenvalue and x is eigenfunction. M , C, and K are matrices. In fluid mechanics we also get such problem where we have to solve the quadratic eigenvalue problem. In my case, I have to solve a polynomial eigenvalue problem similar to (Mλ^2+Cλ+K)x=0, but in my case there are some rows of the matrix M whose all elements are zero. I tried my problem solving using polyeig function but i am getting some eigenvalue as infinity.

M = diag([3 0 3 1]);
C = [0.4 0 -0.3 0;0 0 0 0;-0.3 0 0.5 -0.2;0 0 -0.2 0.2];
K = [-7 2 4 0;2 -4 2 0;4 2 -9 3;0 0 3 -3];
[X,e] = polyeig(K,C,M)
X = 4×8
         0         0    0.2887    0.4940    0.4581   -0.4593    0.2968   -0.4855
    1.0000    1.0000   -0.1210    0.1747    0.4861   -0.4865   -0.1209   -0.1715
         0         0   -0.5307   -0.1446    0.5141   -0.5137   -0.5386    0.1425
         0         0    0.7876   -0.8393    0.5381   -0.5372    0.7792    0.8453
e = 8×1
       Inf
      -Inf
   -2.4145
   -1.6607
   -0.3708
    0.3580
    2.0897
    1.4984

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Answer 1

Sai Kiran 2023-4-26

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Hi,

[X,E] = POLYEIG(A0,A1,..,Ap) solves the polynomial eigenvalue problem of degree p:

(A0 + lambda*A1 + ... + lambda^p*Ap)*x = 0.

The input is p+1 square matrices, A0, A1, ..., Ap, all of the same order, n. The output is an n-by-n*p matrix, X, whose columns are the eigenvectors, and a vector of length n*p, E, whose elements are the eigenvalues.

If A0 or Ap is a singular matrix then you will get some of the eigen values to be infinity. Here M is your Ap and it is a singular matrix.

I hope it helps!

Thanks.