Consider a rotation T(x) = Ajc in R3. (That is, A is an orthogonal 3 x 3 matrix with
Chapter 7, Problem 38(choose chapter or problem)
Consider a rotation T(x) = Ajc in R3. (That is, A is an orthogonal 3 x 3 matrix with determinant 1.) Show that T has a nonzero fixed point [i.e., a vector v with T(v) = 5]. This result is known as Eulers theorem, after the great Swiss mathematician Leonhard Euler (1707-1783). (Hint: Consider the characteristic polynomial fA(k). Pay attention to the intercepts with both axes. Use Theorem 7.1.2.)
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