On the uniqueness of the minimal solution to the matrix polynomial equation A(λ)X(λ)+Y(λ)B(λ)=C(λ)

✍ Scribed by J. Feinstein; Y. Bar-ness

• Publisher: Elsevier Science
• Year: 1980
• Tongue: English
• Weight: 251 KB
• Volume: 310
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(78)90012-1

✦ Synopsis

The uniqueness of the minimal solution of the matrix equation A(A)X(A)+ Y(A)B(h) = C(A) is discussed in this paper. It is proved that Bamett's condition for uniqueness can be obtained when only A(A) or B(A) (not necessarily both) is regular.

Furthermore, it is shown that if such a minimal solution exists, it is not unique if and only if both matrices are nonregular.