Geodesic
Finding a complete set of solutions or proving unsolvability for certain classes of matrix polynomial equations with commuting coefficients
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 12, pp. 1988-1997

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Two classes of matrix polynomial equations with commuting coefficients are examined. It is shown that the equations in one class have complete sets of solutions, whereas the equations in the other class are unsolvable. A method is given for finding the solution set of an equation in the former class. 
@article{ZVMMF_2007_47_12_a2,
     author = {B. Z. Shavarovskii},
     title = {Finding a~complete set of solutions or proving unsolvability for certain classes of matrix polynomial equations with commuting coefficients},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1988--1997},
     publisher = {mathdoc},
     volume = {47},
     number = {12},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_12_a2/}
}
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B. Z. Shavarovskii. Finding a complete set of solutions or proving unsolvability for certain classes of matrix polynomial equations with commuting coefficients. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 12, pp. 1988-1997. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_12_a2/