Journal
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume 128, Issue 5, Pages 1415-1418Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/S0002-9939-99-05233-8
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Norms of idempotents, involutions, and the Hermitian and skew-Hermitian parts of involutions are shown to be elementary trigonometric functions of an angle between two subspaces of Hilbert space. When the spaces involved are nontrivial, the norm of a linear idempotent is the cosecant of the angle between its range and kernel; the norm of a linear involution is the cotangent of half the angle between the involution's eigenspaces.
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