Displaying similar documents to “Decomposition in the large of two-forms of constant rank”

Forms equivalent to curvatures.

Horacio Porta, Lázaro Recht (1986)

Revista Matemática Iberoamericana

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The 2-forms, Ω and Ω' on a manifold M with values in vector bundles ξ --> M and ξ' --> M are equivalent if there exist smooth fibered-linear maps ξ --> ξ' and W: ξ --> ξ' with Ω' = UΩ and Ω = WΩ'. It is shown that an ordinary 2-form equivalent to the curvature of a linear connection has locally a non-vanishing integrating factor at each point in the interior of the set rank (ω) = 2 or in the set rank (ω) > 2. Under favorable conditions the...

Trace and determinant in Banach algebras

Bernard Aupetit, H. Mouton (1996)

Studia Mathematica

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We show that the trace and the determinant on a semisimple Banach algebra can be defined in a purely spectral and analytic way and then we obtain many consequences from these new definitions.

A new rank formula for idempotent matrices with applications

Yong Ge Tian, George P. H. Styan (2002)

Commentationes Mathematicae Universitatis Carolinae

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It is shown that rank ( P * A Q ) = rank ( P * A ) + rank ( A Q ) - rank ( A ) , where A is idempotent, [ P , Q ] has full row rank and P * Q = 0 . Some applications of the rank formula to generalized inverses of matrices are also presented.