This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 1 Homework 6 1. let V = R 2 . none of the the following are innerproducts. for each one, give, with explanation, an axiom which is violated. a. ( u,v ) = u 1 v 1 u 2 v 2 b. ( u,v ) = u 1 v 1 + u 2 v 1 + u 2 v 2 c. ( u,v ) = 0 d. ( u,v ) = u 1 v 2 5. 2. let V = C 3 , with the innerproduct ( u,v ) = u 1 v 1 + 2 u 2 v 2 + u 3 v 3 , and let U = span { (1 , , 1) , (1 ,i, 0) } ⊂ V . find an orthonormal basis of U using gramschmidt. 3. let V = f : [0 , 2 π ] → R f is continuous , the vector space of all continuous realvalued functions on the interval [0 , 2 π ], and define an innerproduct by ( f,g ) = Z 2 π f ( x ) g ( x ) dx. let U be the threedimensional subspace spanned by U = span { 1 , sin , cos } . a. show that { 1 , sin , cos } are an orthogonal basis of U . find and orthonormal basis. b. let f ∈ V be the function f ( x ) = x ≤ x ≤ π 2 π x π < x ≤ 2 π 1 which looks like a tent. find the projection proj U ( f ) of f onto U , and plot a couple points. is it pretty close tocouple points....
View
Full
Document
This note was uploaded on 10/05/2011 for the course MATH 3340 taught by Professor Carlsson during the Spring '11 term at Northwestern.
 Spring '11
 Carlsson
 Linear Algebra, Algebra

Click to edit the document details