what if the some rows of matrix M is zeros

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Chandan
Chandan 2023-4-24
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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Chandan
Chandan 2023-4-24
编辑：Torsten 2023-4-24
Ran in:
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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Sai Kiran
Sai Kiran 2023-4-26
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.

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