Linear Algebra II Problem Set 4 Problem 3: Let f, g be isometries of R³, with fg = gf, and det(f) det (g) = 1. Show that either for g are rotations about the same axis, OR (show) that an ON-basis exists with respect to which both fand g have diagonal shape. Hint: Show that for a rotation A E SO(3), the axis of rotation and the eigenspace from A to eigenvalue are 1 =
Linear Algebra II Problem Set 4 Problem 3: Let f, g be isometries of R³, with fg = gf, and det(f) det (g) = 1. Show that either for g are rotations about the same axis, OR (show) that an ON-basis exists with respect to which both fand g have diagonal shape. Hint: Show that for a rotation A E SO(3), the axis of rotation and the eigenspace from A to eigenvalue are 1 =
Advanced Engineering Mathematics
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ISBN:9780470458365
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Linear Algebra II Problem Set 4
Problem 3:
Let f, g be isometries of IR3, with fg
gf, and det(f)
det(g)
= 1. Show that either f or g are
rotations about the same axis, OR (show) that an ON-basis exists with respect to which both
fand g have diagonal shape.
Hint: Show that for a rotation A e SO(3), the axis of rotation and the eigenspace from A to
eigenvalue are 1
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