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On commutativity of projectors

Radosław Kala (2008)

Discussiones Mathematicae Probability and Statistics

It is shown that commutativity of two oblique projectors is equivalent with their product idempotency if both projectors are not necessarily Hermitian but orthogonal with respect to the same inner product.

On quadratic Hurwitz forms. I

Jiří Gregor (1981)

Aplikace matematiky

Homogeneous quadratic polynomials f in n complex variables are investigated and various necessary and sufficient conditions are given for f to be nonzero in the set Γ ( n ) = z C ( n ) : R e z > 0 . Conclusions for the theory of multivariable positive real functions are formulated with applications in multivariable electrical network theory.

On some algebraic identities and the exterior product of double forms

Mohammed Larbi Labbi (2013)

Archivum Mathematicum

We use the exterior product of double forms to free from coordinates celebrated classical results of linear algebra about matrices and bilinear forms namely Cayley-Hamilton theorem, Laplace expansion of the determinant, Newton identities and Jacobi’s formula for the determinant. This coordinate free formalism is then used to easily generalize the previous results to higher multilinear forms namely to double forms. In particular, we show that the Cayley-Hamilton theorem once applied to the second...

On some identities involving spherical means

Gianfranco Cimmino (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

For every positive definite quadratic form in n variables the reciprocal of the square root of the discriminant is equal to the arithmetic mean of the values assumed by the form on the n - 1 sphere centered at 0 and with radius 1 raised to the ( - n 2 )-th. power. Various consequences are deduced from this, in particular a simplification of some calculations from which one obtains the possibility of solving linear systems using spherical means rather than determinants.

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