Project Problem 2: Prove that Trn: M₁, (R) → R is a linear functional. Example 3) Consider V = P, the set of all polynomials with real coefficients. A linear functional on 1 P is given by integration, p(f) = f(x)dx, where ƒ is a polynomial. A more general form of a linear 0 functional on is given in the next proposition. Proposition 1.3. Let g R → R be a continuous function. Consider P → R given by q(f) =
Project Problem 2: Prove that Trn: M₁, (R) → R is a linear functional. Example 3) Consider V = P, the set of all polynomials with real coefficients. A linear functional on 1 P is given by integration, p(f) = f(x)dx, where ƒ is a polynomial. A more general form of a linear 0 functional on is given in the next proposition. Proposition 1.3. Let g R → R be a continuous function. Consider P → R given by q(f) =
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.4: Linear Transformations
Problem 34EQ
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