Abstract
Let ∧ be a lattice of rank r in ℝn. Let E be a linear manifold through the origin in ℝn, of dimension q, q < r. Assume that we have q linearly independent vectors x (1),..., x (q) in E, such that they form a basis for the lattice ∧ ∩ E. Such a set of vectors will be called a set of primitive vectors. We shall show that there exist r — q vectors y (q+1),..., y (r), such that
form a basis for ∧.
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© 1989 Springer-Verlag Berlin Heidelberg
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Siegel, C.L., Chandrasekharan, K. (1989). Lecture VIII. In: Lectures on the Geometry of Numbers. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-08287-4_8
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DOI: https://doi.org/10.1007/978-3-662-08287-4_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08076-0
Online ISBN: 978-3-662-08287-4
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