Let S be a subspace of an inner product space V Let x1, , xn be an orthogonal basis for 5 and let x V Show that the best least squares approximation to x by elements of S is given by x, X) (xi, )...

Let S be a subspace of an inner product space V. Let {x1,..., xn} be an orthogonal

Question:

Let S be a subspace of an inner product space V. Let {x1,..., xn} be an orthogonal basis for 5 and let x ˆˆ V. Show that the best least squares approximation to x by elements of S is given by

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra with Applications

ISBN: 978-0131857858

7th edition

Authors: Steven J. Leon

See More Books

Question Posted: Jun 13, 2016 12:58 AM

See More Questions

Let W be a subspace of an inner product space V and let {w1, w2, ... wm} be an orthogonal basis for W. Show that if v is any vector in V, then (v, wi) (v, w2) (V, W res
Verify that if W is a subspace of an inner product space V and v is in V, then perpw (v) is orthogonal to all w in W.
Show that if W is a subspace of an inner product space V that is spanned by a set of vectors S, then a vector u in V belongs to W if and only if u is orthougonal to every vector in S.
In the circuit shown in Fig. 19-69, the 33- resistor dissipates 0.50W. What is the battery voltage? 68 52 33 75
Paul Boyer, Fran Carrick, and Ed DiPano are contemplating the formation of a partnership. According to the partnership agreement, Boyer is to invest $60,000 and devote one-half time, Carrick is to...
Briefly describe the four coverages of the Equipment Breakdown Protection Coverage Form. What consequential loss coverages are available by endorsement?
Give reasons both in favor of and against the use of a personal time charge as a cost estimate for a project activity.
Kampa Company and Arbor Company are similar firms that operate in the same industry. Arbor began operations in 2001 and Kampa in 1995. In 2006, both companies pay 7% interest on their debt to...
Flexible Budget In an attempt to improve budgeting, the controller for Meliore, Inc., has developed a flexible budget for overhead costs. Meliore, Inc., makes two types of products, the standard...
A Carnot cycle uses 1.00 mol of a monatomic perfect gas as the working substance from an initial state of 10.0 atm and 600 K. It expands isothermally to a pressure of 1.00 atm (Step 1), and then...
Let x be an element of the inner product space V in Exercise 31, and let p1 and p2 be the projections of x onto S1 and S2, respectively. Show that (a) x = P1 + P2. (b) If x S1, then p1 = 0 and hence...
Let Î¸ be a fixed real number and let (a) Show that {x1, x2) is an orthonormal basis for R2. (b) Verify that c21 + c22 = ||y||2 = y2 + y22 cos sin -sin x,-| cos Xi and
It is argued that hydraulic turbines cannot have an efficiency of 100 percent even in the absence of irreversible losses due to limitation by the second law of thermodynamics. Do you agree? Explain.
CASE 7.2 Oracle Corporation: Share-Based Compensation Effects/Statement of Shareholders' Equity A sales-based ranking of software companies provided by Yahoo! Finance on November 5, Year 8, places...
A manufacturer of ovens sells them for $1,450 each. The variable costs are $800 per unit. The manufacturer's factory has annual fixed costs of $1,735,000. a. Given the expected sales volume of 3,100...
1.1 Explain the vitality of a strategy on businesses like Dell. (15) 1.2 Critically discuss the underlying objectives Dell should follow when formulating its business strategy. (20) 1.3 Discuss the...
Our international business plan involves exporting a sustainable apparel brand from India to UK. We will be exploring this plan in further detail below: Product/ Service: Sustainable clothing line...
If X is a random variable with probability density function f given by: f (x) = 4x 4x 3 when 0 x 1 and 0 otherwise, compute the following quantities: (a) The cumulative distribution function F...
An automobile starter motor has an equivalent resistance of 0.0500 and is supplied by a 12.0-V battery with a 0.0100- internal resistance. (a) What is the current to the motor? (b) What voltage is...
Create an appropriate display of the navel data collected in Exercise 25 of Section 3.1. Discuss any special properties of this distribution. Exercise 25 The navel ratio is defined to be a persons...
Show that the diagonal entries of any hermitian matrix are real.
A complex matrix S is called skew-hermitian if SH = -S. (a) If S is skew-hermitian, show that S2 and iS are hermitian. (b) Show that every n x n complex matrix Z can be written uniquely as Z = V + S,...
Show that the inverse of a unitary matrix is again unitary.
Compute the value of ordinary bonds under the following circumstances assuming that the coupon rate is 0.06:(either the correct formula(s) or the correct key strokes must be shown here to receive...
A tax-exempt municipal bond has a yield to maturity of 3.92%. An investor, who has a marginal tax rate of 40.00%, would prefer and an otherwise identical taxable corporate bond if it had a yield to...
Please note, kindly no handwriting. Q. Suppose a 3 year bond with a 6% coupon rate that was purchased for $760 and had a promised yield of 8%. Suppose that interest rates increased and the price of...

Let S be a subspace of an inner product space V. Let {x1,..., xn} be an orthogonal

Question:

x, X) (xi,%)

Step by Step Answer:

Let By Theorem 558 ...View the full answer

Linear Algebra with Applications

Students also viewed these Linear Algebra questions