Unitary Matrices
Not what you're looking for?
1. show that for a 2x2 unitary matrix its determinant is a complex number of unit modulus
2. Verify that the Pi/2 rotation matrix is orthogonal.
3. Verify that the matrices:
A= 1/sqrt(2) * ( 1 i )
( i 1)
and:
B = 1/2 * ( 1+i 1-i )
( 1-i 1+i )
are unitary. Verify that their determinant is of the form exp (i *theta)
Are they Hemitian?
Purchase this Solution
Solution Summary
The solution discusses the properties of unitary matrices.
Solution Preview
Please see the attached files (.doc and .pdf) for complete solutions.
Let U be a unitary matrix and
Then its conjugate transpose is
Which means:
Where denotes complex conjugation.
And ...
Purchase this Solution
Free BrainMass Quizzes
Intro to the Physics Waves
Some short-answer questions involving the basic vocabulary of string, sound, and water waves.
Classical Mechanics
This quiz is designed to test and improve your knowledge on Classical Mechanics.
The Moon
Test your knowledge of moon phases and movement.
Introduction to Nanotechnology/Nanomaterials
This quiz is for any area of science. Test yourself to see what knowledge of nanotechnology you have. This content will also make you familiar with basic concepts of nanotechnology.
Basic Physics
This quiz will test your knowledge about basic Physics.