Let T be a linear operator on a vector space V, let v be a nonzero vector in V, and let W be the T-cyclic subspace of V generated by v. Prove that (a) W is T-invariant. (b) Any T-invariant subspace of V containing v also contains W.
Let T be a linear operator on a vector space V, let v be a nonzero vector in V, and let W be the T-cyclic subspace of V generated by v. Prove that (a) W is T-invariant. (b) Any T-invariant subspace of V containing v also contains W.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.4: Linear Transformations
Problem 34EQ
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Let T be a linear operator on a
(a) W is T-invariant.
(b) Any T-invariant subspace of V containing v also contains W.
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