Let L be a linear operator on a vector space V. Define Ln, n 1, recursively

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Let L be a linear operator on a vector space V. Define Ln, n ≥ 1, recursively by
L1 = L
Lk+ l(v) = L(Lk(V)) for all v ∈ V
Show that L" is a linear operator on V for each n > 1.

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Linear Algebra with Applications

ISBN: 978-0131857858

7th edition

Authors: Steven J. Leon

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Question Posted: Jun 13, 2016 12:53 AM

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Let L be a linear operator on a vector space V. Define Ln, n 1, recursively

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The proof is by induction on n In the case n 1 L 1 is a linear operator sinc...View the full answer

Linear Algebra with Applications

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