Question: Let Q be an orthogonal matrix. (a) Show that if A is an eigen value of Q then || = I. (h) Show that |

Let Q be an orthogonal matrix.
(a) Show that if A is an eigen value of Q then |λ| = I.
(h) Show that | det (Q)| = 1.

Step by Step Solution

★★★★★

3.42 Rating (161 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a If is an eigenvalue of an orthogonal matrix ... 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

949-M-L-A-E (779).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Let Q be an orthogonal matrix such that QA makes sense. Show that A and QA have the same singular values.

Q:

Let Q be an orthogonal matrix such that QA makes sense. Show that (QA)+ = A+QT.

Q:

Let Q be an orthogonal matrix and let d = det(g). Show that |d| = 1.

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:

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:

1 1. (6+4+4+6) Let P3 denote the vector space of all third degree or less polynomials. (a) Find two linearly independent vectors in P3 that interpolate the data points (1, 2), (2, 1) and (3, 2). (b)...

Q:

Hello, I would like to have the answer to this exercise if possible?From question b to c if it is possible, because for a I was able to answer.I suspect that this exercise seems long. That's why I...

Q:

3 (5 points total) Let A 1 l 3 2 4 I} . 3 2 8 (a) (4 points) Find a basis 3;; for the nullspace of A and 21 basis 83 for the range of A. (b) (1 point] 'What is Rank(A) and Nullity(A)'.' Rank(A) =...

Q:

Exercise 6.8: The QR algorithm In this exercise you'll write a program to calculate the eigenvalues and eigenvectors of a real symmetric matrix using the QR algorithm. The first challenge is to write...

Q:

A quaternion q is an ordered 4-tuple (s,v) = (s,v1,v2,v3) = s*h + v1*i + v2*j + v3*k for vector v = (v1,v2,v3) and unit quaternions h=(1,0,0,0), i=(0,1,0,0), j=(0,0,1,0), k=(0,0,0,1). Multiplication...

Q:

Auditors rely on the audit risk formula to determine the types and amount of audit evidence to collect in order to keep the overall audit risk of engagements to a minimum or below defined tolerable...

Q:

The accurate control of a nuclear reactor is important for power system generators. Assuming the number of neutrons present is proportional to the power level, an ionization chamber is used to...

Q:

The botulinum exotoxin causes _ _ _ _ _ _ _ . Group of answer choicesnone of theseantibiotic associated colitistetanusmuscle contraction

Q:

6. Discuss some of the pros and cons of increasing development assistance, both from the point of view of the donor country and the point of view of the recipient country.

Q:

In each case, show that T is symmetric and find an orthonormal basis of eigenvectors of T. (a) T:(R3R3; T(a, b, c) = (2a + 2r, 3b, 2a + 5c)-, use the dot product (b) T: R3 R3; T(a, b, c) = (7a - b,...

Q:

Let T: M22 -> M22 be given by T(X) = AX, where A is a fixed 2 Ã 2 matrix. (a) Compute MB(T), where Note the order! (b) Show that cT(x) = [CA(x)]2. (c) If the inner product on M22 is (X, Y) =...

Q:

Let T: R 2 R 2 be given by T(a, b) = (b a, a + 2b). Show that T is symmetric if the dot product is used in R 2 but that it is not symmetric if the following inner product is used:

Q:

Rachel is 40 years old. She plans on retiring in 25 years when she will be 65 years old. Rachel believes she will live until she is 95. In order to live comfortably, she needs a substantial...

Q:

Homework - Chapter 13 Seved Help Save & Exit Submit Check my work 3 You have been given the following return information for a mutual fund, the market index, and the risk free rate. You also know...

Q:

Quad Enterprises is considering a new three-year expansion project that requires an initial fixed asset investment of $3 million. The fixed asset will be depreciated straight-line to zero over its...