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FURTHERRESULTSONTHECRAIG-SAKAMOTOEQUATION ELA

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ELA

FURTHER RESULTS ON THE CRAIG-SAKAMOTO EQUATION

∗

JOHN MAROULAS†

Abstract. In this paper, necessary and sufficient conditions are stated for the Craig-Sakamoto equation det(I−sA−tB) =det(I−sA)det(I−tB) to hold for all scalars s, t ∈C. Moreover, spectral properties for matrices A and B that satisfy this equation are investigated.

Key words. Determinant, Characteristic polynomial, Craig-Sakamoto equation, Bilinear form.

AMS subject classifications.15A15, 15A18, 15A63.

∗ Received by the editors September 3, 2007. Accepted for publication September 11, 2008.

Handling Editor: Michael Tsatsomeros.

†Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece ([email protected]). Research supported by a grant of the EPEAEK, project Pythago- ras II. The project is co-funded by the European Social Fund (75%) and GreekNational Resources (25%).

Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society Volume 17, pp. 445-457, September 2008

http://math.technion.ac.il/iic/ela

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