Question: Let x and y be vectors in Rn and let Q be an n x n orthogonal matrix. Show that if z = Qx and

Let x and y be vectors in Rn and let Q be an n x n orthogonal matrix. Show that if
z = Qx and w = Qy
then the angle between z and w is equal to the angle between x and y.

Step by Step Solution

★★★★★

3.50 Rating (173 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

If 1 is the angle between x and y and 2 is the ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

949-M-L-A-E (672).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Let Q be an orthogonal 2 ( 2 matrix and let x and y be vectors in. If ( is the angle between x and y, prove that the angle between Qx and Qy is also (. (This proves that the linear transformations...

Let x and y be vectors in an inner product space. Show that if x y then the distance between x and y is (||x||2 + ||y||2)1/2

Let x and y be vectors in Rn and define (a) Show that p ¥ z. Thus p is the vector projection of x onto y; that is, x = p + z, where p and z are orthogonal components of x, and p is a scalar...

Let A be an n n matrix and let x and y be vectors in Rn. Show that if Ax = Ay and x y, then the matrix A must be singular.

Let r1 ,..., rp be vectors in Rn, and let Q be an m x n matrix. Write the matrix [Qr1 ... Qrp] as a product of two matrices (neither of which is an identity matrix).

THE UNIVERSITY OF NEW SOUTH WALES SCHOOL OF MATHEMATICS AND STATISTICS JUNE 2016 MATH2501 Linear Algebra (1) TIME ALLOWED - THREE HOURS. (2) TOTAL NUMBER OF QUESTIONS - 5 (3) ANSWER ALL QUESTIONS (4)...

Linear algebra with R programming Hi, can you please teach me r codes of Householder decomposition? Thank you. 3. The idea of householder transformation can be used to generate n x n random...

Let Ri denote the simple return on asset i, (i = 1, .-. N) with E[R;] = Hi, var(R;) = 0; and cov(R, R;) = 0ij. Define the N x1 vectors R = (R1, ... , RN)', u = (41, ... ,UN)', x= = (x1, . , XN)', y =...

CS - Linear Algebra 1. Let Q be an n x n matrix with columns q1, . .., In. Suppose Q equals Q-1. . Show that each q; is unit length. . Show that the vectors q's are orthogonal to each other. . Find a...

CS - LINEAR ALGEBRA - 1. Let Q be an n x n matrix with columns q1, . .., In. Suppose Q equals Q-1. . Show that each q; is unit length. . Show that the vectors q's are orthogonal to each other. . Find...

If a clamping force of 300 N is required at A, determine the amount of force F that must be applied to the handle of the toggleclamp. 70 mm -235 mm- 30 mm 275 mm 130 30 rhm

6. two separate samples receive differently treatments. After treatment, the first sample has n = 9 with SS = 462, and the second has n = 7 with SS = 420. Please show all work!!! How you got your...

43. If firms are entering an industry that is monopolistically competitive, we would expect A. the demand for existing firms to shift rightward. B. the market price of the product to increase. C. the...

Depending on the range of experience of the trainer/consultant we hire, we may get the benefit of important insights that will add quality, or we may receive inappropriate or incorrect advice that...

Find the equations of the line of intersection of the following planes. 3x + y - 2z = 1 and x + y + 2 = 5.

Find the angle between the following pairs of vectors. (a) = [3 -1 0]T, = [-6 2 0]T (b) = [2 1 -1]T, = [3 6 3]T (c) = [0 3 4]T, = [52 -7 -1]T

In each case, find all points of intersection of the given plane and the line [x y z]T = [1 -2 3]T + t[2 5 -1]T. (a) 2x - y - z = 5 (b) -x - 4y - 3z = 6

The drop down link for the last questions are listed as: Required rate of return modified internal rate of return (MIRR) internal rate of return (IRR) Thanks! Attempts: Average: 14 7. Understanding...

The Gilead Science Corporation spent several years working on developing a product that can be used to provide a healthy supplement to a variety of food products. The benefits of a new supplement...

answer all pls! Question 31 What are the dividend yield, capital gains yield, and total required rate of return based on the following. PO = $14.00, D1 = $1.20, P1 = $16.00 6.15%, 15.38.%, 21.53.%...