Example 3. The operator Ax = d/dt x(t), defined on the subspace M ofC[0, 1] consisting of all continuously differentiable functions, has rangeC[0, 1]. A is not bounded, however, since elements of arbitrarily smallnorm can produce elements of large norm when differentiated. On theother hand, if A is regarded as having domain D[0, 1] and range C[0, 1],it is bounded with ||A|| = 1.

consider the operator d/dt on C[0, 1] with domain consisting of continuously differentiable…

Answered: Example 3. The operator Ax = d/dt x(t),…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 70EQ

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