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On a criterion of D-stability for P-matrices

Olga Y. Kushel (2016)

Special Matrices

In this paper, we study positive stability and D-stability of P-matrices.We introduce the property of Dθ-stability, i.e., the stability with respect to a given order θ. For an n × n P-matrix A, we prove a new criterion of D-stability and Dθ-stability, based on the properties of matrix scalings.

On a generalization of de Rham lemma

Kyoji Saito (1976)

Annales de l'institut Fourier

Let $M$ be a free module over a noetherian ring. For $ω_{1}, ..., ω_{k} \in M$ , let $𝒜$ be the ideal generated by coefficients of $ω_{1} \land ... \land ω_{k}$ . For an element $ω \in ⋀^{p} M$ with $p < prof . 𝒜$ , if $ω \land ω_{1} \land ... \land ω_{k} = 0$ , there exists $η_{1}, ..., η_{k} \in ⋀^{p - 1} M$ such that $ω = \sum_{i = 1}^{k} η_{i} \land ω_{i}$ .This is a generalization of a lemma on the division of forms due to de Rham (Comment. Math. Helv., 28 (1954)) and has some applications to the study of singularities.

On linear differential equations involving a para-Grassmann variable.

Mansour, Toufik, Schork, Matthias (2009)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

On reducing and deflating subspaces of matrices.

Monov, V., Tsatsomeros, M. (2004)

ELA. The Electronic Journal of Linear Algebra [electronic only]

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...