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. Fix an arbitrary vo € V, and define C(vo) = span {Tk (vo) : ke N}. Show that C(vo) is a T-ambivalent subspace of V, and that it's the smallest T-ambivalent subspace con- taining vo. Recall: To show that C(vo) is the smallest T-ambivalent subspace containing vo, show that if UCV is another other T-ambivalent subspace containing Vo, then C(vo) CU.

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. Fix an arbitrary vo € V, and define C(vo) = span {Tk (vo) : ke N}. Show that C(vo) is a T-ambivalent subspace of V, and that it's the smallest T-ambivalent subspace con- taining vo. Recall: To show that C(vo) is the smallest T-ambivalent subspace containing vo, show that if UCV is another other T-ambivalent subspace containing Vo, then C(vo) CU.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.4: Linear Transformations

Problem 24EQ

See similar textbooks