Abstract. We study the SVD of an arbitrary matrix , especially its subspaces of activation, which leads in natural manner to pseudoinverse of Moore-Bjenhammar-Penrose. Besides, we analyze the compatibility of linear systems and the uniqueness of the corresponding solution, and our approach gives the Lanczos classification for these systems.
If Ω/F is a Galois extension with Galois G and μ(Ω) denotes the group of roots of unity in Ω, we use the group Z1 (G,μ(Ω)) of crossed homomorphisms to study radical extensions inside Ω. Furthermore, we characterise cubic radical extension, and we provide an example to show that this result can not extended for higher degree extensions.
Abstract:In this paper, we study the Singular Value Decomposition of an arbitrary matrix A , especially its subspaces of activation, which leads in natural manner to the pseudo inverse of Moore -Bjenhammar -Penrose. Besides, we analyze the compatibility of linear systems and the uniqueness of the corresponding solution and our approach gives the Lanczos classification for these systems.
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