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About the von Neumann regularity of triangular block matrices. (English) Zbl 1002.15001
The authors study von Neumann regularity of block matrices over rings in terms of properties of the blocks. Particular attention is paid to block triangular and Toeplitz matrices. As an application, the Drazin invertibility of some companion matrices is considered.

MSC:
15A09 Theory of matrix inversion and generalized inverses
15B57 Hermitian, skew-Hermitian, and related matrices
15B33 Matrices over special rings (quaternions, finite fields, etc.)
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[1] Ben-Israel, A.; Greville, T.N.E., Generalized inverses: theory and applications, (1974), Wiley New York · Zbl 0305.15001
[2] Huylebrouck, D.; Puystjens, R., Generalized inverses of a sum with a radical element, Linear algebra appl., 84, 289-300, (1986) · Zbl 0611.15006
[3] Prasad, K.M., Generalized inverses of matrices over commutative rings, Linear algebra appl., 211, 35-52, (1994) · Zbl 0811.15004
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[5] R. Puystjens, M.C. Gouveia, Drazin invertibility for matrices over an arbitrary ring, 1999, submitted · Zbl 1056.15005
[6] Puystjens, R.; Hartwig, R.E., The group inverse of a companion matrix, Linear and multilinear algebra, 43, 137-150, (1997) · Zbl 0890.15003
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