= 4. Let P₂ be the vector space of real polynomials of degree at most 2, that is P₂ = {ao + a₁ + a₂x²2 a, ER}. Consider the inner product on P₂ defined by Define T: P2 P₂ by (p\q) = p(x)q(x) dx. 0 T(ao + ax + a2x²) = a₁x. (a) Show that T is not Hermitian (i.e. self-adjoint). (b) Consider the basis B = {1, x, x2} for P₂. Show that the matrix [T]g is Hermitian. Explain why this does not contradict with result from Part (a).

= 4. Let P₂ be the vector space of real polynomials of degree at most 2, that is P₂ = {ao + a₁ + a₂x²2 a, ER}. Consider the inner product on P₂ defined by Define T: P2 P₂ by (p\q) = p(x)q(x) dx. 0 T(ao + ax + a2x²) = a₁x. (a) Show that T is not Hermitian (i.e. self-adjoint). (b) Consider the basis B = {1, x, x2} for P₂. Show that the matrix [T]g is Hermitian. Explain why this does not contradict with result from Part (a).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 15EQ

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