Question: If Q is an orthogonal n ( n matrix and {v1( ( ( ( ( vk} is an orthonormal set in, prove that {Q v1(

If Q is an orthogonal n ( n matrix and {v1( ( ( ( ( vk} is an orthonormal set in, prove that {Q v1( ( ( ( ( Q vk} is an orthonormal set.

R

R"

Step by Step Solution

★★★★★

3.47 Rating (160 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

We must show that Qv i Qv j 0 for i j and that Qv i Qv i 1 Since ... View full answer

blur-text-image
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)

Word file Icon

859-L-A-L-S (2687).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Prove that if Q is an orthogonal n n matrix, then its Frobenius norm is ||Q||F = n.

Q:

Prove Theorem 9.10. Theorem 9.10 Suppose that Q is an orthogonal n n matrix. Then (i) Q is invertible with Q1 = Qt; (ii) For any x and y in Rn, (Qx)t Qy = xty; In addition, the converse of part (i)...

Q:

If Q is an n ( n matrix such that the angles (Qx, Qy) and (x, y) are equal for all vectors x and y in , prove that Q is an orthogonal matrix.

Q:

7. Suppose we have the female population of a species is divided into juveniles, yearlings, and adults and that each year . 90 percent of the juveniles live to be yearlings. . 80 percent of the...

Q:

how to slove problem 3 and 4 GENERAL INSTRUCTION You should submit your homework online. No so hard copy is accepted. e only accepted format is pdf. You can sean your work in pdf using a smartphone,...

Q:

How to slove question 3 and 4 GENERAL INSTRUCTION You should submit your homework online. No so hard copy is accepted. e only accepted format is pdf. You can sean your work in pdf using a smartphone,...

Q:

9, DUE Friday, March 24th, 2017 Hand in Part A and Part B as two separate assignments. Include the following information in the top left corner of every assignment: your full name, instructor's last...

Q:

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

Q:

Math 110 Homework Assignment 9 due date: Nov. 18, 2016 1. (a) Prove or disprove: the vectors ~v1 = (2, 3) and ~v2 = (1, 5) form a basis for R2 . (b) Prove or disprove: the vectors w ~ 1 = (1, 9) and...

Q:

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)...

Q:

You've completed your slide show on the agile organization, and you've been looking forward to giving the presentation for the first time. The presentation is going along nicely until you notice one...

Q:

As USA Today looks toward its future, a number of issues must be considered. Toward this end, the latter half of the case is written in the form of a situation analysis. Students should be encouraged...

Q:

If you are gradually vested in a retirement plan over a 4 - year period, the plan is a cliff plan. contributory plan. self - directed plan. graded plan. maximum vesting plan.

Q:

Suppose that growing corn requires only two inputs: land and labor. A researcher obtains data on 100 farms of varying sizes located on roughly equally fertile land. In a bivariate regression of corn...

Q:

If A is a square matrix whose rows add up to the zero vector, explain why A cannot be invertible.

Q:

Construct standard parity check and generator matrices for a (15, 11) Hamming code.

Q:

In Theorem 3.37, prove that if B = A, then PGx = 0 for every x in Z k 2 . (Throughout this proof we denote by ai the ith column of a matrix A.) With P and G as in the statement of the theorem, assume...

Q:

This information relates to Ivanhoe Co. 1. 2. 3. 4 On April 5, purchased merchandise from Pharoah Company for $24.200 on account. On April 7. purchased equipment on account for $25,800. On April 8,...

Q:

It says "Mark owns a 20% interest in a partnership (not real estate) in which his at-risk amount is $44000 at the beginning of the year. During the year, the partnership borrows $90000 on a recoursw...

Q:

QUESTIONS Vrterest id or accrued during 2018 on regate quistion deteness of million or enim formare persone con is deductible wrate de interest QUESTIONS