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Real Linear Substitutions with Equimodular Multipliers, and their expression in terms of their Invariants

Published online by Cambridge University Press:  20 January 2009

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§1. Let

denote a linear substitution of non-vanishing determinant; and let the roots k of its characteristic equation

be for the present assumed distinct. Then with each root k is associated an invariant point or poleP, and a linear invariant, or invariant (n−2)-plane ξ. If the n points P do not lie on an (n−2)-plane, the determinant of their coordinates,

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1916

References

page 20 note * Hilton, , Linear Substitutions, p. 12, Ex. 7.Google Scholar

page 21 note * Scott, , Determinants, p. 81.Google ScholarPubMed

page 21 note † Hilton, ibid., p. 26.

page 28 note * For a case with no real linear invariants, but ½ n real quadratic invariants, see below, § 10.

page 33 note * Salmon-Rogers, , Analytical Geometry of Three Dimensions (1912), §79.Google Scholar

page 33 note † See, e.g., Routh, Advanced Rigid Dynamics, §269.

page 40 note * See also Bell, Coordinate Geometry of Three Dimensions, §§ 166–8; Salmon-Rogers, § 202.