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

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

Step by Step Solution

★★★★★

3.55 Rating (166 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

If Q q 1 q 2 q n is o... 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 (2933).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

(a) Prove that if Q is an orthogonal matrix, then ||Qx|| = ||x|| for any vector x Rn, where |||| denotes the standard Euclidean norm. (b) Prove the converse: if ||(Qx|| = ||x|| for all x Rn, then Q...

Q:

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"

Q:

If Q is an orthogonal matrix, prove that any matrix obtained by rearranging the rows of Q is also orthogonal.

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:

Exercise 22.11. This exercise leads through a direct argument, without reference to Gram-Schmidt, in the case of invertible square matrices that QR-decompositions are uniquely determined. That is, if...

Q:

In mathematics, a matrix (plural matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. In this exercise, you are supposed to write a C program for matrix...

Q:

Chapter 7.1 Write on paper for upvote. questions: 1, 3 , 5, 11, 12, 26 please -145 -1455 - 1450 H O O HIN O HIN -NO InNo -No (6) HIN #ND HID Into O O a. for every vector x in R". As a first step in...

Q:

You must create ONE .pdfile that contains the following: Page 1 will be your report - the TA will only read and mark page 1 - if there is additional writing on any other page, it will be ignored and...

Q:

Problem 4 (PROBABILISTIC LATENT VARIABLE MODEL AND ITS RELATION TO PCA) Consider the latent variable model x=Wz+e, (12) where I E Rd, 2 E R9W E Rdxq and e E Rd. The probabilistic model uses z ~...

Q:

THE UNIVERSITY OF NEW SOUTH WALES SCHOOL OF MATHEMATICS AND STATISTICS JUNE 2015 MATH2501 Linear Algebra (1) TIME ALLOWED - THREE HOURS. (2) TOTAL NUMBER OF QUESTIONS - 5 (3) ANSWER ALL QUESTIONS (4)...

Q:

Expand your answer to Problem 27.10 by showing the structural formula for each dipeptide in a manner that reveals the stereochemistry at the -carbon atom. Problem 27.10 Write structural formulas...

Q:

On 01 November 2020, Palm Ltd purchased 75% of Sandwort Ltd. The statements of profit or loss for the year ended 31 March 2021 of the two entities are as follows: 1. The group depreciation policy is...

Q:

Fill in the missing words: An activity is any discrete- that an organization to make or deliver a or service.

Q:

Name and explain the four market factors that affect price planning. (25.2)

Q:

Find (fo g) (x) and (go f) (x).

Q:

Find the domain of (fo g) (x) and the domain of (go f) (x).

Q:

Use a graphing calculator to find the intervals on which the function f(x) = x3 + 4x2 is increasing or decreasing, and find any relative maxima or minima.

Q:

question 7: If Miguel only needs to save $3,500 for his down payment and wants to accomplish this goal in less than 3 years, which of the above savings accounts is the better option? O The standard...

Q:

Woodpecker, Inc., stock has an annual return mean and standard deviation of 11.2 percent and 57 percent, respectively. What is the smallest expected loss in the coming month with a probability of 5.0...

Q:

Calculation of HomeNets Free Cash Flow (Including Cannibalization and Lost Rent), Using Revision, assume SG&A expnses paid in Cash to Parent 1. What is the IRR? 2.What is the NPV when cost of capital...