Jordan normal form projections
نویسندگان
چکیده
منابع مشابه
Jordan Normal Form
This paper outlines a proof of the Jordan Normal Form Theorem. First we show that a complex, finite dimensional vector space can be decomposed into a direct sum of invariant subspaces. Then, using induction, we show the Jordan Normal Form is represented by several cyclic, nilpotent matrices each plus an eigenvalue times the identity matrix – these are the Jordan
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This paper presents a method based on elementary transformations which may be applied to a matrix A, whose characteristic polynomial has been decomposed into linear factors, in order to obtain a nonsingular matrix P such that P-1AP is in Jordan normal form. This method can be used in the classroom, among other problems, to directly solve a linear ODE with constant coefficients. We also present ...
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In this paper it is shown that the use of Jordan normal form instead of Hermite normal form would improve substantially the efficiency and the security of the lattice based signature scheme. In this scheme we also use a new hash function in such a way that the efficiency improved is obtain without decreasing the security of the function.
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Let β1, . . . , βn be linearly independent vectors in a vector space. For all j with 0 ≤ j ≤ n and all vectors α1, . . . , αk, if β1, . . . , βn are in the span of β1, . . . , βj, α1, . . . , αk, then j + k ≥ n. The proof of the claim is by induction on k. For k = 0, the claim is obvious since β1, . . . , βn are linearly independent. Suppose the claim is true for k−1, and suppose that β1, . . ....
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ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 1988
ISSN: 0003-889X,1420-8938
DOI: 10.1007/bf01194566