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Unformatted text preview: PHYS 455 Homework I Assigned: October 4, 2011, Tuesday. Due: October 12, 2011, Wednesday. Notes: (i) You can discuss and solve the problems together with your friends. However, you should write your own solution on your homework. Directly copying other people’s solutions kills millions of brain cells and is considered harmful to your health. (ii) The solutions will be posted to the web page http://www.physics.metu.edu.tr/˜sturgut/p455/. No late homeworks will be accepted after the solutions is posted. (iii) Excessive usage of papers is harmful to our trees. Do not write every detail in presenting your solutions. 1. The eigenvalue equation. Consider the following 3 × 3 matrix. A = 0 0 1 0 1 0 1 0 0 We will solve the eigenvalue equation for this matrix. (a) Compute the characteristic polynomial and find the eigenvalues (hint: all are inte- gers). Is there any degenerate eigenvalue? (b) Find all of the eigenvectors and normalize them but answer the following as well....
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- Spring '11
- Linear Algebra, Hilbert space, Orthonormal basis, Hilbert space H., space H. Let