منابع مشابه
.1 Kronecker's Approximation Theorem
Theorem 2 (Kronecker Approximation Theorem (1884)) ∃x ∈ Z s.t. Ax = b if and only if ∀y, y>b is an integer whenever y>A is an integral vector. Proof: To prove the forward implication, take an integral solution x∗. For any y, since y>Ax∗ = y>b, if y>A is integral then y>b must be an integer too. We next prove the converse. First, suppose that Ax = b does not have a solution (over the reals). The...
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ژورنال
عنوان ژورنال: Indagationes Mathematicae
سال: 2016
ISSN: 0019-3577
DOI: 10.1016/j.indag.2016.02.002