Answer Exercise 10.1.28 when T is an arbitrary nonsingular 2 × 2 matrix. Use Exercise 8.5.19.
In Exercise 10.1.28
Let T be a positive definite 2 × 2 matrix. Let En = (Tnx | ||x|| = 1], n = 0, 1,2.......be the image of the unit circle under the nth power of T.
(a) Prove that En is an ellipse.
True or false:
(b) The ellipses En all have the same principal axes.
(c) The semi-axes are given by rn = rn1 sn = sn1.
(d) The areas are given by An = ?an where ? = A1/?.
This question was answered on: Jul 11, 2017
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