Suppose V is a vector space and T: V → V is a linear operator. A subspace UCV is said to be T-ambivalent if T(U) CU. Show that ker(T) and im(T) are T-ambivalent.
Suppose V is a vector space and T: V → V is a linear operator. A subspace UCV is said to be T-ambivalent if T(U) CU. Show that ker(T) and im(T) are T-ambivalent.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Suppose V is a vector space and T: V → V is a linear operator. A subspace U CV is said
to be T-ambivalent if T(U) CU.
Show that ker(T) and im(T) are T-ambivalent.
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