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i) Show that the set of translations in space (in two or three dimensions) forms a group for a given group operation. Explain what is the group operation (group law) and give an explicit example. ii) Same questions for the rotations in the plane about a fixed axis. One could choose the plane to be the (x, y) plane and the axis to be along the z-direction.

i) Show that the set of translations in space (in two or three dimensions) forms a group for a given group operation. Explain what is the group operation (group law) and give an explicit example. ii) Same questions for the rotations in the plane about a fixed axis. One could choose the plane to be the (x, y) plane and the axis to be along the z-direction.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Groups and transformations. i) Show that the set of translations in space (in two or three dimensions) forms a group for a given group operation. Explain what is the group operation (group law) and give an explicit example. ii) Same questions for the rotations in the plane about a fixed axis. One could choose the plane to be the (x, y) plane and the axis to be along the z-direction.
Transcribed Image Text:Groups and transformations. i) Show that the set of translations in space (in two or three dimensions) forms a group for a given group operation. Explain what is the group operation (group law) and give an explicit example. ii) Same questions for the rotations in the plane about a fixed axis. One could choose the plane to be the (x, y) plane and the axis to be along the z-direction.
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