Let T: C′[0, 1]→C[0, 1] be the linear transformation T( f ) = f ′. Show that λ = 1 is an eigenvalue of T with corresponding eigenvector f (x) = ex.
Let T: C′[0, 1]→C[0, 1] be the linear transformation T( f ) = f ′. Show that λ = 1 is an eigenvalue of T with corresponding eigenvector f (x) = ex.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.3: Matrices For Linear Transformations
Problem 52E: Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.
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Let T: C′[0, 1]→C[0, 1] be the linear transformation T( f ) = f ′. Show that λ = 1 is an eigenvalue of T with corresponding eigenvector f (x) = ex.
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