Question

If A and B are conjugate matrices they have the same eigenvectors.

If A and B are conjugate matrices they have the same eigenvectors.

Math   Algebra   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Solution:

NO. Conjugate matrices do not have same eigen vector. For that let and are two conjugate matrices. Then there exist an invertible matrix such that   . Now let be an eigen vector of the matrix corresponding to the eigen value . Then we have

This show that is an eigen vector of the matrix corresponding to the same eigen value . Thus conjugate matrices have same eigen value but not necessarily same eigen vector.

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
We say two n × n matrices A and B are similar if there is an...
We say two n × n matrices A and B are similar if there is an invertible n × n matrix P such that A = PBP^ -1. a) Show that if A and B are similar n × n matrices, then they must have the same determinant. b) Show that if A and B are similar n × n matrices, then they must have the same eigenvalues. c) Give an example to show that A and B can be...
Calculate the eigenvalues and eigenvectors of the following matrices. B = a11=c, a12=m a21=-m and a22=c...
Calculate the eigenvalues and eigenvectors of the following matrices. B = a11=c, a12=m a21=-m and a22=c   
Let matrices A,B∈Mn×n(R). Show that if A and B are each similar to some diagonal matrix,...
Let matrices A,B∈Mn×n(R). Show that if A and B are each similar to some diagonal matrix, and also have the same eigenvectors (but not necessarily the same eigenvalues), then  AB=BA.
Normalize the eigenvectors of the Pauli matrices. Choose the phases such that the first non-vanishing element...
Normalize the eigenvectors of the Pauli matrices. Choose the phases such that the first non-vanishing element of each vector is real and positive.
Problem 30. Show that if two matrices A and B of the same size have the...
Problem 30. Show that if two matrices A and B of the same size have the property that Ab = Bb for every column vector b of the correct size for multiplication, then A = B.
Hi, I know that if two matrices A and B are similar matrices then they must...
Hi, I know that if two matrices A and B are similar matrices then they must have the same eigenvalues with the same geometric multiplicities. However, I was wondering if that statement was equivalent. In order terms, if two matrices have the same eigenvalues with the same geometric multiplicities, must they be similar? If not, is it always false?
Hi, I know that if two matrices A and B are similar matrices then they must...
Hi, I know that if two matrices A and B are similar matrices then they must have the same eigenvalues with the same geometric and algebraic multiplicities. However, I was wondering if that statement was equivalent. In order terms, if two matrices have the same eigenvalues with the same algebraic multiplicities, must they be similar? What about geometric multiplicities?
Normally, we start with a matrix and find the eigenvalues and eigenvectors. But it’s interesting to...
Normally, we start with a matrix and find the eigenvalues and eigenvectors. But it’s interesting to see if this process can be performed in reverse. Suppose that a 2x2 matrix has eigenvalues of +2 and -1 but no info on the eigenvectors. Can you find the matrix? How many matrices would have these eigenvalues?
Normally, we start with a matrix and find the eigenvalues and eigenvectors. But it’s interesting to...
Normally, we start with a matrix and find the eigenvalues and eigenvectors. But it’s interesting to see if this process can be performed in reverse. Suppose that a 2x2 matrix has eigenvalues of +2 and -1 but no info on the eigenvectors. Can you find the matrix? How many matrices would have these eigenvalues?
We have Hermitian operators A and B with x as a complx. conjugate. Explain: Is A+B...
We have Hermitian operators A and B with x as a complx. conjugate. Explain: Is A+B always hermitian? Is xB always hermitian? Is AB always Hermitian?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT