(f) Let T: V→ V be linear on the finite dimensional vector space V and v € Va nonzero vector. Give examples where the cyclic subspace generated by v either coincides or is larger than the cyclic subspace generated by T(v).

(f) Let T: V→ V be linear on the finite dimensional vector space V and v € Va nonzero vector. Give examples where the cyclic subspace generated by v either coincides or is larger than the cyclic subspace generated by T(v).

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 74E: Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors...

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Linear Algebra Help! f)

(f) Let T: V→ V be linear on the finite dimensional vector space V and v € Va nonzero vector.
Give examples where the cyclic subspace generated by v either coincides or is larger than the
cyclic subspace generated by T(v).

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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