Abstract
If T ∈ O(ℛ2), then T is completely determined by its action on the basis vectors e l = (1, 0) and e 2 = (0, 1). If Te 1 = (µ, v), then µ 2 + v 2 = 1 and Te 2 = ±(−v, µ), since T preserves length and orthogonality. Choose θ, 0 ≤ θ < 2π, such that cos θ = µ and sin θ = v.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1985 Springer Science+Business Media New York
About this chapter
Cite this chapter
Grove, L.C., Benson, C.T. (1985). Finite Groups in Two and Three Dimensions. In: Finite Reflection Groups. Graduate Texts in Mathematics, vol 99. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-1869-0_2
Download citation
DOI: https://doi.org/10.1007/978-1-4757-1869-0_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3072-9
Online ISBN: 978-1-4757-1869-0
eBook Packages: Springer Book Archive