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The group SO(1,2) is defined as SO(1,2)= {A E GL3(R): ATnA = n}, where is the diagonal matrix η with entries (-1,1,1) on the diagonal. Show that the set /1 + a² -α² ²1-a² -α X = -{(the α :) :GER} a 1 forms a subgroup of SO(1,2). To show that X is a subgroup, you need to show that each matrix from X is an element of SO(1,2), that the set of such matrices is closed and that it contains inverses.

The group SO(1,2) is defined as SO(1,2)= {A E GL3(R): ATnA = n}, where is the diagonal matrix η with entries (-1,1,1) on the diagonal. Show that the set /1 + a² -α² ²1-a² -α X = -{(the α :) :GER} a 1 forms a subgroup of SO(1,2). To show that X is a subgroup, you need to show that each matrix from X is an element of SO(1,2), that the set of such matrices is closed and that it contains inverses.

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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The group SO(1,2) is defined as SO(1,2)= {A E GL3(R): ATnA = n}, where is the diagonal matrix η with entries (-1,1,1) on the diagonal. Show that the set /1 + a² -α² ²1-a² -α X = -{(the α :) :GER} a 1 forms a subgroup of SO(1,2). To show that X is a subgroup, you need to show that each matrix from X is an element of SO(1,2), that the set of such matrices is closed and that it contains inverses.
Transcribed Image Text:The group SO(1,2) is defined as SO(1,2)= {A E GL3(R): ATnA = n}, where is the diagonal matrix η with entries (-1,1,1) on the diagonal. Show that the set /1 + a² -α² ²1-a² -α X = -{(the α :) :GER} a 1 forms a subgroup of SO(1,2). To show that X is a subgroup, you need to show that each matrix from X is an element of SO(1,2), that the set of such matrices is closed and that it contains inverses.
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