Geodesic
Common eigenvalues of two matrices
Dalʹnevostočnyj matematičeskij žurnal, Tome 13 (2013) no. 1, pp. 52-60.

Voir la notice de l'article provenant de la source Math-Net.Ru

A new approach to determine common eigenvalues of two matrices is proposed. The algorithm is based on the criteria for the existence of common eigenvalues of matrices in the form of algebraic equation depending on their elements and on the properties of solutions of the matrix equation $AX=XB$. The method for constructing a polynomial whose roots equal to the common eigenvalues of matrices $A$ and $B$ is presented. 
@article{DVMG_2013_13_1_a4,
     author = {E. A. Kalinina},
     title = {Common eigenvalues of two matrices},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {52--60},
     publisher = {mathdoc},
     volume = {13},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2013_13_1_a4/}
}
TY  - JOUR
AU  - E. A. Kalinina
TI  - Common eigenvalues of two matrices
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2013
SP  - 52
EP  - 60
VL  - 13
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2013_13_1_a4/
LA  - ru
ID  - DVMG_2013_13_1_a4
ER  - 
%0 Journal Article
%A E. A. Kalinina
%T Common eigenvalues of two matrices
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2013
%P 52-60
%V 13
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2013_13_1_a4/
%G ru
%F DVMG_2013_13_1_a4
E. A. Kalinina. Common eigenvalues of two matrices. Dalʹnevostočnyj matematičeskij žurnal, Tome 13 (2013) no. 1, pp. 52-60. http://geodesic.mathdoc.fr/item/DVMG_2013_13_1_a4/

[1] M. Bokher, Vvedenie v vysshuyu algebru, GTTI, M.-L., 1933

[2] E. Dzhuri, Innory i ustoichivost dinamicheskikh sistem, Nauka, M., 1979

[3] E. A. Kalinina, A. Yu. Uteshev, Teoriya isklyucheniya. Ucheb. posobie, NII Khimii SPbGU, SPb., 2002

[4] C. C. MacDuffee, The Theory of Matrices, Chelsea Publishing Company, N.-Y., 1956

[5] K. Datta, “An algorithm to determine if two matrices have common eigenvalues”, IEEE Transactions on Automatic Control, 27:5 (1982), 1131–1133 | DOI | MR | Zbl

[6] T. D. Roopamala, S. K. Katti, “New Approach to Identify Common Eigenvalues of real matrices using Gerschgorin Theorem and Bisection method”, (IJCSIS) International Journal of Computer Science and Information Security, 7:2 (2010)

[7] F. R. Gantmakher, Teoriya matrits, Nauka, M., 1967 | MR