2. Let A: V→ V be a linear map. Show that the following statements areequivalent:(a) 0 is an isolated fixed point of A.(b) A – I:V –→ Vis an isomorphism.(c) 0 is a Lefschetz fixed point of A.(d) A is a Lefschetz map.

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Description: 2. Let A: V→ V be a linear map. Show that the following statements areequivalent:(a) 0 is an isolated fixed point of A.(b) A – I:V –→ Vis an isomorphism.(c) 0 is a Lefschetz fixed point of A.(d) A is a Lefschetz map.

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2. Let A: V – V be a linear map. Show that the following statements are equivalent: (a) 0 is an isolated fixed point of A. (b) A – 1:V → V is an isomorphism. (c) 0 is a Lefschetz fixed point of A. (d) A is a Lefschetz map.

2. Let A: V – V be a linear map. Show that the following statements are equivalent: (a) 0 is an isolated fixed point of A. (b) A – 1:V → V is an isomorphism. (c) 0 is a Lefschetz fixed point of A. (d) A is a Lefschetz map.

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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2. Let A: V→ V be a linear map. Show that the following statements are
equivalent:
(a) 0 is an isolated fixed point of A.
(b) A – I:V –→ Vis an isomorphism.
(c) 0 is a Lefschetz fixed point of A.
(d) A is a Lefschetz map.

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