Question: Let U be an n n orthogonal matrix. Show that the rows of U form an orthonormal basis of R n .

Let U be an n × n orthogonal matrix. Show that the rows of U form an orthonormal basis of Rn.

Step by Step Solution

★★★★★

3.44 Rating (154 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

To show that the rows of an n n orthogonal matrix U form an orthonormal basis of Rn we need to demon... 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

Students Have Also Explored These Related Linear Algebra And Its Applications Questions!

Q:

Let U be an m-dimensional subspace of Rn and let V be a k-dimensional subspace of U, where 0

Q:

Let U be an n n upper triangular matrix with nonzero diagonal entries. (a) Explain why U must be nonsingular. (b) Explain why U-1 must be upper triangular.

Q:

Let U be an n x n orthogonal matrix. Show that if {v 1 ,........,v n } is an orthonormal basis for R n , then so is {Uv 1,.........., Uv n }.

Q:

1. Let B = (v1, .... Un), C= {ul,....un}, and D = (w1,..., Win} be three bases for R". (a) Prove the following identity regarding the change of basis matrices: Pc +DPBAC = l'B +D. (b) Consider the...

Q:

5. The following series of questions explores the relationship between the standard dot product on R" (geometry) and linear operators on R" (linear algebra). Let U be a n x n matrix, and think of it...

Q:

Theorem 6.14 (Schur). Let T be a linear operator on a nite- dimensional inner product space V. Suppose that the characteristic poly- nomial of T splits. Then there exists an orthonormal basis 7 for V...

Q:

Part II (20%) True or False. For each statement, select T if the statement is true (in all cases), or select T if false (for at least one example). No justication needed. 6- (a) T F If a set of m...

Q:

1. Let A = 90 3 552 Find the characteristic polynomial of A and guess one of its roots by looking at integer divisors of the constant term. Find an eigenvector corresponding to this eigenvalue, and...

Q:

Hi i need help with the problems highlighted and circled in red, its only linear algebra 176 CHAPTER 2 Matrices and Linear Transformations 4. Give the domain and codomain of the matrix transforma- In...

Q:

5. The goal of this question is to prove the following characterization of bases. Proposition 1. Vectors v1, ..., Uk in R" form a basis of R" if and only if they satisfy the following universal...

Q:

What benefits can be attained when a leader is involved in negotiating? How does it relate to power?

Q:

If you were the lawyer who presided the case of the land dispute in Calamba, will you side to Dominicans who have done favors to keep your position, or to your fellow townsfolk who demand an...

Q:

A program begins executing and waits for the user to input an integer value, however, the user inputs a string variable. This type of error is called a: a . Logic error b . Syntax error c . Runtime...

Q:

=+3.24 People suffering from Alzheimers disease often have difficulty performing basic activities of daily living (ADLs). In one study (Functional Status and Clinical Findings in Patients with...

Q:

List some similarities and differences between this research question and our first research question looking at the average difference in first and second E. coli counts. Lets look at one last...

Q:

Use the Descriptive Statistics applet to create a dotplot of the flow rates. Include average and standard deviation for the fl ow rate. What do you observe?

Q:

Carry out an appropriate test of significance to see whether the Cameroon water filters (population) tend to fl ow at a rate different than 1,000 mL/min, or is an average of 1,000 mL/min plausible?...

Q:

I need a full answer with the worksheet, thank you On December 1, Year 1, John and Patty Driver formed a corporation called Susquehanna Equipment Rentals. The new corporation was able to begin...

Q:

Mariya Company uses a job-order costing system and applies manufacturing overhead cost to jobs on the basis of the cost of direct materials used in production. Its predetermined overhead rate was...

Q:

Consider the following information: Rate of Return if State Occurs 6:33 Probability of State of Economy 0.10 0.60 0.30 State of Economy Recession Normal Boom Stock B -0.21 Stock A 0.04 0.07 0.15 0.14...