Exercise 9.4.11

Avg difficulty 3.0

Let $k$ be a positive integer, let $W_{k}\subseteq\mathbf{Seq}_{K}$ be the subspace consisting of all sequences that are periodic with period $k$ (see Exercise 38). Find a basis for $W_{k}$ . What is its dimension?
More difficult: find a basis for the infinite-dimensional vector space consisting of all periodic sequences of all periods.

Selinger, Matrix Theory and Linear Algebra, Vector spaces, Basis and dimension, Exercise 9.4.11

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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.