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Exercise 10.1.6

Avg difficulty 3.0

Consider the shift function shift⁡:SeqK→SeqK\operatorname{shift}:\mathbf{Seq}_{K}\to\mathbf{Seq}_{K} from Example 10.8. Find a basis for the solution space of each of the following equations:

  1. shift⁡(a)=a\operatorname{shift}(a)=a.

  2. shift⁡(a)=−a\operatorname{shift}(a)=-a.

  3. shift⁡(shift⁡(a))=shift⁡(a)+2a\operatorname{shift}(\operatorname{shift}(a))=\operatorname{shift}(a)+2a.

Selinger, Matrix Theory and Linear Algebra, Linear transformation of vector spaces, Definition and examples, Exercise 10.1.6

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Adapted from Matrix Theory and Linear Algebra © 2017–2026 Peter Selinger, Lyryx Learning, and Ken Kuttler. Licensed under CC BY 4.0. Source: Matrix Theory and Linear Algebra. Imported at revision d74bc3a.