Question

Prove or disprove: there is an inner product on R2 such that the associated norm is...

Prove or disprove: there is an inner product on R2 such that the associated norm is given by ∥(x1, x2)∥ = |x1| + |x2| for all (x1, x2) ∈ R2.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Prove/disprove the following claim: If R1 and R2 are integral domains, then R1 ⊕ R2 must...
Prove/disprove the following claim: If R1 and R2 are integral domains, then R1 ⊕ R2 must also be an integral domain under the operations • (r1,r2)+(s1,s2)=(r1 +s1,r2 +s2) • (r1,r2)·(s1,s2)=(r1 ·s1,r2 ·s2)
3. a. Consider R^2 with the Euclidean inner product (i.e. dot product). Let v = (x1,...
3. a. Consider R^2 with the Euclidean inner product (i.e. dot product). Let v = (x1, x2) ? R^2. Show that (x2, ?x1) is orthogonal to v. b. Find all vectors (x, y, z) ? R^3 that are orthogonal (with the Euclidean inner product, i.e. dot product) to both (1, 3, ?2) and (2, 7, 5). C.Let V be an inner product space. Suppose u is orthogonal to both v and w. Prove that for any scalars c and d,...
Let S ∈ L(R2) be given by S(x1, x2) = (x1 +x2, x2) and let I...
Let S ∈ L(R2) be given by S(x1, x2) = (x1 +x2, x2) and let I ∈ L(R2) be the identity operator. Using the inner product defined in problem 1 for the standard basis and the dot product, compute <S, I>, || S ||, and || I || {Inner product in problem 1: Let W be an inner product space and v1, . . . , vn a basis of V. Show that <S, T> = <Sv1, T v1> +...
Prove the Inner Product Properties.
Prove the Inner Product Properties.
Let W be an inner product space and v1,...,vn a basis of V. Show that〈S, T...
Let W be an inner product space and v1,...,vn a basis of V. Show that〈S, T 〉 = 〈Sv1, T v1〉 + . . . + 〈Svn, T vn〉 for S,T ∈ L(V,W) is an inner product on L(V,W). Let S ∈ L(R^2) be given by S(x1, x2) = (x1 + x2, x2) and let I ∈ L(R^2) be the identity operator. Using the inner product defined in problem 1 for the standard basis and the dot product, compute 〈S,...
Say (V,<,>) is a finite dimensional real inner product space. Then the composition of two self...
Say (V,<,>) is a finite dimensional real inner product space. Then the composition of two self adjoint operators is again self adjoint. Prove or Disprove.
Use the inner product (u, v) = 2u1v1 + u2v2 in R2 and the Gram-Schmidt orthonormalization...
Use the inner product (u, v) = 2u1v1 + u2v2 in R2 and the Gram-Schmidt orthonormalization process to transform {(?2, 1), (2, 5)} into an orthonormal basis. (Use the vectors in the order in which they are given.) u1 = ___________ u2 = ___________
Use the inner product u, v = 2u1v1 + u2v2 in R2 and the Gram-Schmidt orthonormalization...
Use the inner product u, v = 2u1v1 + u2v2 in R2 and the Gram-Schmidt orthonormalization process to transform   {(2, ?1), (2, 6)}  into an orthonormal basis. (Use the vectors in the order in which they are given.) u1 = u2 =
Use the inner product <u,v>= 2u1v1 + u2v2 in R2 and the Gram-Schmidt orthonormalization process to...
Use the inner product <u,v>= 2u1v1 + u2v2 in R2 and the Gram-Schmidt orthonormalization process to transform {(2, ?1), (2, 6)} into an orthonormal basis. (Use the vectors in the order in which they are given.) u1 = u2 =
let v be an inner product space with an inner product(u,v) prove that ||u+v||<=||u||+||v||, ||w||^2=(w,w) ,...
let v be an inner product space with an inner product(u,v) prove that ||u+v||<=||u||+||v||, ||w||^2=(w,w) , for all u,v load to V. hint : you may use the Cauchy-Schwars inquality: |{u,v}|,= ||u||*||v||.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT