Question: 5. Diagonalizaton via. unitary transform. Consider a 2 x 2 matrix cos sinvi Q- ( sin9 0086 > (a) Show Q is unitary. (b) Show

5. Diagonalizaton via. unitary transform. Consider a 2 x 2 matrix cos sinvi Q- ( sin9 0086 > (a) Show Q is unitary. (b) Show its two eigenvalues are e\" and 8'\"; find the corresponding eigen vectors. [Feel free to work with matrices, and choose your own phase factor for the eigen vectors.) (c) From the eigenvectors, construct the unitary matrix U so that it diagonalizes , UTQU: ( em 0. ) 0 871.3 [The columns of U are nothing but the eigenvectors of 9. This is explained in Sakurai 1.5.3. Use this example to verify it is true.)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock 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

Students Have Also Explored These Related Physics Questions!

Consider the trigonometric series a0 2 + X r=1 (ar cos rx + br sin rx) where a0, a1, a2, . . . and b1, b2, . . . are constants and suppose that f(x) is a periodic function of x with period 2. (a)...

Here are definitions of sequences and trees with integer elements: type iseq = Nil | Cons of int * (unit -> iseq) type itree = Leaf of int | Branch of itree * itree (a) In an ascending sequence such...

Eigenvalue/Eigenvector Part IV: Suppose A is an n x n matrix. a. What does it mean to say that a vector x E Rn is an eigenvector of A? b. Suppose A E R is an eigenvalue of A. What is the eigenspace...

Miller-Rabin test to check whether a number N is composite. This will involve computing a N1 mod N for some value of a. [10 marks] Carry out the steps for N = 65 and a = 1, 2, 8 and 12. on what each...

In a Hopfield neural network configured as an associative memory, with all of its weights trained and fixed, what three possible behaviours may occur over time in configuration space as the net...

can someone solve this Modern workstations typically have memory systems that incorporate two or three levels of caching. Explain why they are designed like this. [4 marks] In order to investigate...

.QUESTION .all the questions to be thoroughly explained Invocations of its type operations involve no writes to persistent memory and no output to clients. Concurrent processes may invoke the object....

) Consider integer division of one two's-complement binary number by another. Programming languages may vary in the result when one argument is negative. What differing conventions might they be...

(a) How does the use of condition codes complicate the implementation of a superscalar processor that supports out-of-order execution? [4 marks] (b) A branch predictor with a high prediction accuracy...

^^^^^ solve please Postopening Scenario: Your angel investors are silent in relation to the business; however, they require board meetings. for status updates on the company's nancial health....

Draw and explain the flowchart for instruction cycle.

The council members of a small town have decided that the earth levee that protects .the town from a nearby river should be rebuilt and strengthened. The town engineer estimates that the cost of the...

Duration is the sensitivity of bond price to interest rate change. Duration over - estimates

Cufford Clark is a recent retiree who is interested in investing some of his savings in corporate bonds. His financial planner has suggested the following bonds: - Bond A has a 13% annual coupon,...

LO14.1 Describe the characteristics of oligopoly.

2. Suppose that the most popular car dealer in your area sells 10 percent of all vehicles. If all other car dealers sell either the same number of vehicles or fewer, what is the largest value that...

2. Compare the elasticity of a monopolistic competitors demand with that of a pure competitor and a pure monopolist. Assuming identical long-run costs, compare graphically the prices and outputs that...