Question

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> + . . . + <Svn, T vn> for S, T ∈ L(V, W) is an inner product on L(V,W).}

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
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,...
Let V = W = R2. Choose the basis B = {x1, x2} of V ,...
Let V = W = R2. Choose the basis B = {x1, x2} of V , where x1 = (2, 3), x2 = (4,−5) and choose the basis D = {y1,y2} of W, where y1 = (1,1), y2 = (−3,4). Find the matrix of the identity linear mapping I : V → W with respect to these bases.
5. Prove or disprove the following statements. (a) Let L : V → W be a...
5. Prove or disprove the following statements. (a) Let L : V → W be a linear mapping. If {L(~v1), . . . , L( ~vn)} is a basis for W, then {~v1, . . . , ~vn} is a basis for V. (b) If V and W are both n-dimensional vector spaces and L : V → W is a linear mapping, then nullity(L) = 0. (c) If V is an n-dimensional vector space and L : V →...
Let T ∈ L(R2) be the linear transformation T(x1, x2) = (3x1 + 2x2, −4x1 −...
Let T ∈ L(R2) be the linear transformation T(x1, x2) = (3x1 + 2x2, −4x1 − 3x2), v = (1, −1), and p(z) = z^2 − 3z + 2. Compute p(T), show that p(T)v = 0, and show that NOT all the roots of p(z) are eigenvalues of T.
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 V1 = R4 and V2 = R2. Let T : V1 → V2 be the...
Let V1 = R4 and V2 = R2. Let T : V1 → V2 be the map dened by T x1 x2 x3 x4 = x1 −x2 + x4 x1 + x2 + x3 + x4 . (a) Show that T is a linear transformation. (b) Let u1 = 1 0 0 −1 , u2 = 0 1 −2 1 .Show that ( u1, u2) is a basis of kerT. (c) Show that imT = V2. (Hint: Compute T(e1) and...
Let V=R2 with the standard scalar multiplication and nonstandard addition given as follows: (x1, y1)⊕(x2, y2)...
Let V=R2 with the standard scalar multiplication and nonstandard addition given as follows: (x1, y1)⊕(x2, y2) := (x1x2, y1+y2). Show that (V,⊕, .) is not a vector space.
first use Gram-Schmidt on x1, x2 to create orthogonal vectors v1 and v2 with the same...
first use Gram-Schmidt on x1, x2 to create orthogonal vectors v1 and v2 with the same span as x1, x2. Now use the formula p =((y, v1)/(v1, v1))v1 + ((y, v2)/(v2, v2))v2 to compute the projection of y onto that span. Of course, replace the inner product with the dot product when working with standard vectors 1) Compute the projection of y = (1, 2, 3)  onto span (x1, x2) where x1 =(1, 1, 1) x2 =(1, 0, 1) The inner...
T/ F : Let V be an inner product space with orthogonal basis B = {v1,...
T/ F : Let V be an inner product space with orthogonal basis B = {v1, . . . , vn}. Let [v]B = (1, 2, 2, 0, . . . , 0). Then ||v|| = 3. The ans is F , but I don't understand why. Please explain.
first use Gram-Schmidt on x1, x2 to create orthogonal vectors v1 and v2 with the same...
first use Gram-Schmidt on x1, x2 to create orthogonal vectors v1 and v2 with the same span as x1, x2. Now use the formula p =((y, v1)/(v1, v1))v1 + ((y, v2)/(v2, v2))v2 to compute the projection of y onto that span. Of course, replace the inner product with the dot product when working with standard vectors 2) Compute the projection of y = (1, 2, 2, 2, 1)  onto span (x1, x2) where x1 =(1, 1, 1, 1, 1)   x2 =(4,...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT