Question: If P is a triangular orthogonal matrix, show that P is diagonal and that all diagonal entries are 1 or -1.

If P is a triangular orthogonal matrix, show that P is diagonal and that all diagonal entries are 1 or -1.

Step by Step Solution

★★★★★

3.47 Rating (167 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Let P be orthogonal so P 1 P T If P is upper triangular so also ... 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

950-M-L-A-L-S (6611).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Let Q be an n à n orthogonal matrix. Show that (a) ||Q|| = 1 (b) cond2(Q) = 1 (c) For any b Rn, the relative error in the solution to Qx = b is equal to the relative residual; that is,1 ell...

Q:

Show that if Q is a proper orthogonal matrix, and R is obtained from Q by interchanging two rows, then R is an improper orthogonal matrix.

Q:

Show that the eigenvalues of the upper triangular Matrix are λ = a and λ = d, and find the corresponding a b A =

Q:

Eigenvectors and Eigenvalues of a Decomposition of a Symmetric Matrix 1/3 puntos (calificado) Let ARdd be a symmetric matrix, and suppose that A=PDPT where - P is a dd orthogonal matrix, and - D is a...

Q:

76. If P is a symmetric orthogonal matrix, show that the characteristic roots ( are either +1 or -1. If P I, show that P has at least one root of each.

Q:

Could you please help with question 326? Thanks Exercise 309 Exercise 310 Theorem 3 Exercise 311 Exercise 312 75 5.8 Real symmetric matrices Real symmetric matrices play the role of real numbers in...

Q:

Could you please help with question 324 and 325? Thanks Exercise 309 Exercise 310 Theorem 3 Exercise 311 Exercise 312 75 5.8 Real symmetric matrices Real symmetric matrices play the role of real...

Q:

Could you please help with question 327 and 328? Thanks Exercise 309 Exercise 310 Theorem 3 Exercise 311 Exercise 312 75 5.8 Real symmetric matrices Real symmetric matrices play the role of real...

Q:

Could you please help with question 322 and 323? Thanks Exercise 309 Exercise 310 Theorem 3 Exercise 311 Exercise 312 75 5.8 Real symmetric matrices Real symmetric matrices play the role of real...

Q:

Could you please help with question 319 and 320 and 321? Thanks No need to all three. Exercise 309 Exercise 310 Theorem 3 Exercise 311 Exercise 312 75 5.8 Real symmetric matrices Real symmetric...

Q:

The phase line in Exercise 11. From the given phase-line diagram, sketch a possible graph of the rate of change of x as a function of x. start here x=2 x=4 8

Q:

Study the case in detail, and specifically, the advice of Miller's uncle, Mert a. For this case, you are required to critically assess the decision of Miller's proposed recapitalization involved...

Q:

A _ _ _ _ _ _ _ _ _ _ rate is a theoretical interest rate at which an investor is guaranteed to earn the subscribed rate and at which the borrower will never default. Question 3 5 options: a ) risk -...

Q:

The Author will deliver to the Publisher on a mutually agreeable date one copy of the manuscript of the Work as finally arranged by the editor and satisfactory to the Publisher in form and...

Q:

Let V be the subspace of the vector space of all real-valued continuous functions that has basis S = {et, e-t}. Show that V and R2 are isomorphic.

Q:

Let S = (v1, v2, ( ( (( vn) be an ordered basis for the n-dimensional vector space V, and let v and w be two vectors in V. Show that v = w if and only if [v]S = [w]S.

Q:

Show that if S is an ordered basis for an n-dimensional vector space V, v and w are vectors in V, and c is a scalar, then And [v+w], = [v]s+[w],

Q:

Topic: Measures of position for ungrouped data Answer the following: Independent Assessment 2 Direction. Miggy has an assignment that is to ask at random 20 students in their school about their ages....

Q:

1. Problem 2-39 Innis Investments manages funds for a number of companies and wealthy clients. The investment strategy is tailored to each client's needs. For a new client, Innis has been authorized...

Q:

Larry is implementing a FaaS ( firewall - as - a - service ) on his network. Where will this firewall sit?Group of answer choiceson the cloudon a hypervisorinside a portin the browser