Question

Let X be the vector space of all ordered pairs of complex numbers. Can we obtain...

Let X be the vector space of all ordered pairs of complex numbers. Can we obtain the norm defined on ||x||=|ξ_1 |+|ξ_2 | where x=(ξ_1,ξ_2) from an inner product?

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 X be the vector space of all ordered pairs of complex numbers. Can we obtain...
Let X be the vector space of all ordered pairs of complex numbers. Can we obtain the norm defined on ||x||=|ξ_1 |+|ξ_2 | where x=(ξ_1,ξ_2) from an inner product?
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...
Consider the set of all ordered pairs of real numbers with standard vector addition but with...
Consider the set of all ordered pairs of real numbers with standard vector addition but with scalar multiplication defined by  k(x,y)=(k^2x,k^2y). I know this violates (alpha + beta)x = alphax + betax, but I'm not for sure how to figure that out? How would I figure out which axioms it violates?
Let V be the set of all ordered pairs of real numbers. Consider the following addition...
Let V be the set of all ordered pairs of real numbers. Consider the following addition and scalar multiplication operations V. Let u = (u1, u2) and v = (v1, v2). • u ⊕ v = (u1 + v1 + 1, u2 + v2 + ) • ku = (ku1 + k − 1, ku2 + k − 1) Show that V is not a vector space.
Are the following vector space and why? 1.The set V of all ordered pairs (x, y)...
Are the following vector space and why? 1.The set V of all ordered pairs (x, y) with the addition of R2, but scalar multiplication a(x, y) = (x, y) for all a in R. 2. The set V of all 2 × 2 matrices whose entries sum to 0; operations of M22.
Let V be the set of all ordered pairs of real numbers. Consider the following addition...
Let V be the set of all ordered pairs of real numbers. Consider the following addition and scalar multiplication operations V. Let u = (u1, u2) and v = (v1, v2). • u ⊕ v = (u1 + v1 + 1, u2 + v2 + ) • ku = (ku1 + k − 1, ku2 + k − 1) 1)Show that the zero vector is 0 = (−1, −1). 2)Find the additive inverse −u for u = (u1, u2). Note:...
Question 1:  Is there a vector space that can not be an inner product space? Justify your...
Question 1:  Is there a vector space that can not be an inner product space? Justify your answer. Part 2: Suppose that u and v are two non-orthogonal vectors in an inner product space V,< , >. Question 2: Can we modify the inner product < , > to a new inner product so that the two vectors become orthogonal? Justify your answer.
Let V be a vector space: d) Suppose that V is finite-dimensional, and let S be...
Let V be a vector space: d) Suppose that V is finite-dimensional, and let S be a set of inner products on V that is (when viewed as a subset of B(V)) linearly independent. Prove that S must be finite e) Exhibit an infinite linearly independent set of inner products on R(x), the vector space of all polynomials with real coefficients.
A2. Let v be a fixed vector in an inner product space V. Let W be...
A2. Let v be a fixed vector in an inner product space V. Let W be the subset of V consisting of all vectors in V that are orthogonal to v. In set language, W = { w LaTeX: \in ∈V: <w, v> = 0}. Show that W is a subspace of V. Then, if V = R3, v = (1, 1, 1), and the inner product is the usual dot product, find a basis for W.
Let (V, C) be a finite-dimensional complex inner product space. We recall that a map T...
Let (V, C) be a finite-dimensional complex inner product space. We recall that a map T : V → V is said to be normal if T∗ ◦ T = T ◦ T∗ . 1. Show that if T is normal, then |T∗(v)| = |T(v)| for all vectors v ∈ V. 2. Let T be normal. Show that if v is an eigenvector of T relative to the eigenvalue λ, then it is also an eigenvector of T∗ relative to...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT