Let A be an n x n real matrix with the property that AT A Show that if Ax x for some nonzero vector x in Cn, then, in fact, A is real and the real part of x is an eigenvector of A ...

x T Ax x T x x T because x is an eigenvector It is easy to see ...

Let A be an n x n real matrix with the property that AT = A. Show

Question:

Let A be an n x n real matrix with the property that AT = A. Show that if Ax = λx for some nonzero vector x in Cn, then, in fact, A is real and the real part of x is an eigenvector of A.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra and Its Applications

ISBN: 978-0321791542

4th edition

Authors: David C. Lay

See More Books

Question Posted: May 02, 2016 12:07 PM

See More Questions

Let x and y be distinct vectors in Rn (that is, x y) and let A be an n n matrix with the property that Ax = Ay. Show that det(A) = 0.
Let A be an n x n matrix and let Q and V be n n orthogonal matrices. Show that (a) ||QA||2 = ||A||2 (b) ||AV||2 = ||A||2 (c) ||QAV||2 = ||A||2
Let A be an n x n matrix and let A he a nonzero elgenvalue of A. Show that if x is an eigene.1or belonging to A, then x is in the column space of A. Hence the eigenspace corresxponding to is a...
A bond currently has a price of $940. The current yield to maturity on the bond is 7%. If the yield decreases by 20 basis points, the price of the bond will go up to $960. Based on this information,...
According to the Bureau of Labor Statistics, the average annual salary of a worker in Detroit, Michigan, is $35,748. Suppose the median annual salary for a worker in this group is $31,369 and the...
What types of products are bartered?
A randomized block design was used to compare the mean responses of three treatments. Four blocks of three homogeneous experimental units were selected, and each treatment was randomly assigned to...
Maturity The Dorsett Corporation issued $600,000 of 13% bonds on January 1, 2006 for $614,752.24. The bonds are due December 31, 2008, were issued to yield 12%, and pay interest semiannually on June...
Case You are working as a financial advisor for Mr . Buzzi, who is a well - known investor. Today Mr . Buzzi has explained to you a new business project that he has, and he wants you to prepare...
Describe in words what the state machine in Figure 3.69 does. Using binary state encodings, complete a state transition table and output table for the FSM. Write Boolean equations for the next state...
Let A be an n x n real matrix with the property that AT = A, let x be any vector in Cn, and let q = xrAx. The equalities below show that q is a real number by verifying that q = q. Give a reason for...
Let A be a real n x n matrix, and let n x n be a vector in Cn. Show that Re(Ax) = A(Re x) and Im(Ax) = A(Im x).
Distinguish between direct and indirect segment costs. LO.1
31. What is meant by path? 32. Give the formula for calculating D4 and D8 distance. 33. What is geometric transformation? 34. What is image translation and scaling? 35. Define the term Luminance
1. Explain Brightness adaptation and Discrimination 2.Explain sampling and quantization:
3. Explain about Mach band effect? 4. Explain color image fundamentals. 5. Explain CMY model.
1. Describe the fundamental steps in image processing? 2. Explain the basic Elements of digital image processing:
3. Explain the Structure of the Human eye 4. Explain the RGB model
In Problems 5964, construct a truth table to verify the implication or equivalence. PVqpq
Outline some of the major problems confronting an international advertiser.
Concern a simple model of the national economy described by the difference equation Here Y k is the total national income during year k, a is a constant less than 1, called the marginal propensity to...
Recall from calculus that integrals such as are tedious to compute. (The usual method is to apply integration by parts repeatedly and use the half-angle formula.) Use the matrix P or P -1 . To...
Concern a simple model of the national economy described by the difference equation Here Y k is the total national income during year k, a is a constant less than 1, called the marginal propensity to...
How does budgeting household expenses differ from budgeting business expenses? What are the similarities?
This is a partial adjusted trial batance of Cullumber Compary manualys
Which of the following journal entries will record the payment of a $1,500 salaries payable originally incurred for Salaries Expense? Select one: A. Debit Salaries Expense; credit Salaries Payable B....

Let A be an n x n real matrix with the property that AT = A. Show

Question:

Step by Step Answer:

x T Ax x T x x T because x is an eigenvector It is easy to see ...View the full answer

Linear Algebra and Its Applications

Students also viewed these Linear Algebra questions