Question

In C 2 , show that hx, yi = xA∗y is an inner product, where A...

In C 2 , show that hx, yi = xA∗y is an inner product, where A = 3 1 + i 1 − i 1

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
Non Euclidean Geometry Show that if z=x+yi with y>0, then |U(z)|<1, where U(z)= (iz+1)/(z+i)
Non Euclidean Geometry Show that if z=x+yi with y>0, then |U(z)|<1, where U(z)= (iz+1)/(z+i)
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 V be a finite dimensional vector space over R with an inner product 〈x, y〉...
Let V be a finite dimensional vector space over R with an inner product 〈x, y〉 ∈ R for x, y ∈ V . (a) (3points) Let λ∈R with λ>0. Show that 〈x,y〉′ = λ〈x,y〉, for x,y ∈ V, (b) (2 points) Let T : V → V be a linear operator, such that 〈T(x),T(y)〉 = 〈x,y〉, for all x,y ∈ V. Show that T is one-to-one. (c) (2 points) Recall that the norm of a vector x ∈ V...
prove that: x^3+y^3=(x+y)(x+yi)(x+yi^2)
prove that: x^3+y^3=(x+y)(x+yi)(x+yi^2)
Suppose 〈 , 〉 is an inner product on a vector space V . Show that...
Suppose 〈 , 〉 is an inner product on a vector space V . Show that no vectors u and v exist such that ∥u∥ = 1, ∥v∥ = 2, and 〈u, v〉 = −3.
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,...
F(x, y) = yi + xj (a) Show F is conservative Given your answer in (a)...
F(x, y) = yi + xj (a) Show F is conservative Given your answer in (a) show that the following integrals have the same value. (b) The line segment y = x from (0,0) to (1,1). (c) The parabola y=x^2 from (0,0) to (1,1). (d) The cubic y=x^3 from (0,0) to (1,1). (e) The b, c and d are examples of what property resulting from part a?
(i) Let u= (u1,u2) and v= (v1,v2). Show that the following is an inner product by...
(i) Let u= (u1,u2) and v= (v1,v2). Show that the following is an inner product by verifying that the inner product hold <u,v>= 4u1v1 + u2v2 +4u2v2 (ii) Let u= (u1, u2, u3) and v= (v1,v2,v3). Show that the following is an inner product by verifying that the inner product hold <u,v> = 2u1v1 + u2v2 + 4u3v3
Regression: !Y=Bo + B1Xi +ui Randon Sample of 3 observations on Xi and Yi Yi Xi...
Regression: !Y=Bo + B1Xi +ui Randon Sample of 3 observations on Xi and Yi Yi Xi 51 3 60 2 45 4 a) Compute the OLS estimate Bo and B1 b) Compute the predicted value ŷi and the residual (u-hat)i for each of the 3 observations c) What is the mean of the (u-hat)i's? d) What is the mean of the ŷi's? How does it compare to the mean of the Yi's?
Let X=2N={x=(x1,x2,…):xi∈{0,1}} and define d(x,y)=2∑(i≥1)(3^−i)*|xi−yi|. Define f:X→[0,1] by f(x)=d(0,x), where 0=(0,0,0,…). Prove that maps X onto...
Let X=2N={x=(x1,x2,…):xi∈{0,1}} and define d(x,y)=2∑(i≥1)(3^−i)*|xi−yi|. Define f:X→[0,1] by f(x)=d(0,x), where 0=(0,0,0,…). Prove that maps X onto the Cantor set and satisfies (1/3)*d(x,y)≤|f(x)−f(y)|≤d(x,y) for x,y∈2N.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT