Purchase Solution

Orthonormal Bases : Projection

Not what you're looking for?

Ask Custom Question

Please see the attached file for full problem description.

1. Let Complex 3-space C^3 be equipped with the standard inner product and let W be the subspace of C^3 that is spanned by u_1= (1, 0, 1) and u_2= (1/3, 1/3, -1/3). Project the vector v= (1, i, i) onto W. Show work.

Help:
: is the square root of

Attachments
Purchase this Solution
Solution Summary

A projection is calculated from an inner product using Gram-Schmidt. The solution is detailed and well presented.

Solution Preview

Please see the attached file for the full solution.

Thanks for using BrainMass.

1. Let Complex 3-space C^3 be equipped with the standard inner product and let W be the subspace of C^3 that is spanned by u_1= ...

Purchase this Solution
Free BrainMass Quizzes
Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Probability Quiz

Some questions on probability

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

View More Free Quizzes
Related BrainMass Solutions

  • Vector Subspace, Orthonormal Basis, Othogonal Projection and Inner Product

    158492 Vector Subspace, Orthonormal Basis, Othogonal Projection and Inner Product Let W be the subspace of R^2 spanned by the vector (3, 4). Using the standard inner product, let E be the orthogonal projection of R^2 onto W.

  • Inner Product Space, Finite Dimensional Subspace, Orthonormal Basis and Orthogonal Projections

    (a) Prove that (b) Prove that is the orthogonal projection on (c) Prove that for every . If , then . Proof: (a) Because is an orthonormal basis, then for each , , we have Thus for any , we have . This implies that .

  • Linear Algebra: Orthogonal Bases

    175274 Linear Algebra: Orthogonal Bases Let A be an n X n matrix and, as usual, let a_1, ..., a_n denote its column vectors. a. Suppose a_1,...,a_n form an orthonormal set. Show that A^-1 = A^T. b. Suppose a_1,...

  • Normalized kets

    Let { |u1 , | u2 , | u3 } be an orthonormal basis of this space. The kets | phi0 ? and | phi1 ? are defined by: | phio = (1/sqrt2 ) | u1 + (i/2) | u2 + (1/2) | u3 | phi1 = (1/sqrt3 ) | u1 + (i/sqrt3) | u3 1.Are these kets normalized?

  • bases of the kernel and image of the orthogonal projection

    Find bases of the kernel and image of the orthogonal projection onto the YZ-axis in R^3. Please see the attachment. The bases of the kernel and image of the orthogonal projection are embedded.

  • Fourier series expansions

    Find the Fourier series expansions of f(x) = Co + C1x^2 with respect to the following two orthonormal bases on the interval [0,L] (L>0) a) {(1/L)^.5, (2/L)^.5*cos*((k*pi*x)/L)|k=1,2,...} b) {(2/L)^.5*sin*((k*pi*x)/L)|k=1,2,....}.

  • Operators and eigenvectors

    If we want to project on some subspace of Hilbert space, we can simply take a set of orthonormal basis vectors of that subspace |e_n> and construct the projection operator: P = sum over n of |e_n> is an arbitrary element of Hilbert

  • Orthogonal basis and matrix, Gram-Schmidt process

    Let T: R^3 -> R^3 be the orthogonal projection on the yz-plane. Find the matrix for T relative to the standard basis for R^3, and then find the matrix for T relative to the basis v1 = (1,0,0), v2 = (1,1,0), and v3 = (1,1,1). 7.

  • Unitary matrix

    So if we consider an orthonormal basis in each of this spaces, together those bases will give us an orthonormal basis for the whole C^n which is what we wanted.

View More Related Solutions