Geodesic
Eigenvalue problem for an irregular $\lambda$-matrix
Zapiski Nauchnykh Seminarov POMI, Computational methods and automatic programming, Tome 58 (1976), pp. 80-92 
V. N. Kublanovskaya; V. B. Mikhailov; V. B. Khazanov. Eigenvalue problem for an irregular $\lambda$-matrix. Zapiski Nauchnykh Seminarov POMI, Computational methods and automatic programming, Tome 58 (1976), pp. 80-92. http://geodesic.mathdoc.fr/item/ZNSL_1976_58_a9/
@article{ZNSL_1976_58_a9,
     author = {V. N. Kublanovskaya and V. B. Mikhailov and V. B. Khazanov},
     title = {Eigenvalue problem for an irregular $\lambda$-matrix},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {80--92},
     year = {1976},
     volume = {58},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_58_a9/}
}
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The solution of the eigenvalue problem is examined for the polynomial $D(\lambda)=A_0\lambda^2+A_1\lambda+A_2$ when the matrices $A_0$ and $A_2$ (or one of them) are singular. A normalized process is used for solving the problem, permitting the determination of linearly independent eigenvectors corresponding to the zero eigenvalue of matrix $D(\lambda)$ and to the zero eigenvalue of matrix $A_0$. The computation of the other eigenvalues of $D(\lambda)$ is reduced to the same problem for a constant matrix of lower dimension. An ALGOL program and test examples are presented.