Question: Suppose V R n is an invariant subspace for the n n matrix T governing the linear iterative system u (k+1) = Tu

Suppose V ⊂ Rⁿ is an invariant subspace for the n × n matrix T governing the linear iterative system u^(k+1) = Tu^(k). Prove that if u⁽⁰⁾∈ V , then so is the solution: u^(k) ∈ V.

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