Question

show that a real 2x2 matrix is normal if and only if it is either symmetric...

show that a real 2x2 matrix is normal if and only if it is either symmetric or has the form a b -b a (in matrix form)

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

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
Show that there is no matrix with real entries A, such that A^2 = [ 0...
Show that there is no matrix with real entries A, such that A^2 = [ 0 1 0 0 ]. (its a 2x2 matrix)
Suppose A is a real 2x2 matrix with complex eigenvalues α ± i β , β...
Suppose A is a real 2x2 matrix with complex eigenvalues α ± i β , β ≠ 0. It was shown in class that the corresponding eigenvectors will be complex. Suppose that a + i b is an eigenvector for α + i β , for some real vectors a , b . Show that a − i b is an eigenvector corresponding to α − i β . Hint: properties of the complex conjugate may be useful. Please show...
For some nonzero 2x2 matrix, with its entries in an integral domain, show that the matrix...
For some nonzero 2x2 matrix, with its entries in an integral domain, show that the matrix is a zero divisor IFF det=0. Show an example!
PCA uses the fact that the correlation matrix is real and symmetric. Are the corresponding eigen...
PCA uses the fact that the correlation matrix is real and symmetric. Are the corresponding eigen values real and distinct? How do you prove that assertion?       
n×n-matrix M is symmetric if M = M^t. Matrix M is anti-symmetric if M^t = -M....
n×n-matrix M is symmetric if M = M^t. Matrix M is anti-symmetric if M^t = -M. 1. Show that the diagonal of an anti-symmetric matrix are zero 2. suppose that A,B are symmetric n × n-matrices. Prove that AB is symmetric if AB = BA. 3. Let A be any n×n-matrix. Prove that A+A^t is symmetric and A - A^t antisymmetric. 4. Prove that every n × n-matrix can be written as the sum of a symmetric and anti-symmetric matrix.
Give an example of a nondiagonal 2x2 matrix that is diagonalizable but not invertible. Show that...
Give an example of a nondiagonal 2x2 matrix that is diagonalizable but not invertible. Show that these two facts are the case for your example.
1. If A is an n n matrix, prove that (a) ATA is a symmetric matrix....
1. If A is an n n matrix, prove that (a) ATA is a symmetric matrix. (b) A + AT is a symmetric matrix and A - AT is a skew-symmetric matrix. (c) A is the sum of a symmetric and a skew-symmetric matrix.
1. Let A be the 2x2 matrix in M_{2x2}(C), whose first row is (0,1) and second...
1. Let A be the 2x2 matrix in M_{2x2}(C), whose first row is (0,1) and second row is (-1,0). (a) Show that A is normal. (b) Find (complex) eigenvalues of A. (c) Find an orthogonal basis for C^2, which consists of eigenvectors of A. (d) Find an orthonormal basis for C^2, which consists of eigenvectors of A.
Suppose A is a 2x2 matrix whose eigenvalues all have negative real parts. For the system...
Suppose A is a 2x2 matrix whose eigenvalues all have negative real parts. For the system x 0 = Ax, is the origin stable or unstable?
3.35 Show that if A is an m x m symmetric matrix with its eigenvalues equal...
3.35 Show that if A is an m x m symmetric matrix with its eigenvalues equal to its diagonal elements, then A must be a diagonal matrix.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT