Abstract
Let G = GLn(R) or SLn(R) and Γn = GLn(Z). Let Posn(R) be the space of positive symmetric real n × n matrices. Recall that symmetric real n × n matrices Z have an ordering, defined by Z ≧ 0 if and only if 〈Zx, x〉 ≧ 0 for all x ∈ Rn. We write Z1 ≧ Z2 if and only if Z1 - Z2 ≧ 0. If Z ≧ 0 and Z is non-singular, then Z ≫ 0, and in fact Z ≧ λI if λ is the smallest, necessarily positive, eigenvalue.
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© 2005 Springer-Verlag Berlin/Heidelberg
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Jorgenson, J., Lang, S. (2005). GLn(R) Action on Posn(R). In: Posn(R) and Eisenstein Series. Lecture Notes in Mathematics, vol 1868. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11422372_1
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DOI: https://doi.org/10.1007/11422372_1
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25787-5
Online ISBN: 978-3-540-31548-3
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