Basis and diagonalization

Assignment Help Mathematics

Reference no: EM13124901

Let T be an element of L(C^3) [complex 3-tuples] be the operator defined by

T(z_1, z_2, z_3) = (z_2, z_3, z_1).

a) Write the matrix of T in the standard basis of C^3.

b Find all eigenvalues of T

c) Is there a basis of C^3 such that the matrix of T in that basis is diagonal? If your answer is "NO", explain why.

If your answer is "YES", write down the matrix in that basis.

Reference no: EM13124901

Questions Cloud

Finite dimensional space and nullity : Let V be a finite-dimensional real (i.e. F = R) vector space. Let T be an element of L(V)(set of operators on V), and assume that T^2 = 0.

Calculate sampling interval and sample size : The auditors wish to test the valuation of accounts receivable in the audit of Seaside Enterprises. The client has $5,000,000 of total recorded receivables, composed of 2500 accounts.

Yogurt machine and gross income : Only executives are permitted to buy yogurt machines at a discount. What is Sarah's adjusted basis for the yogurt machine and how much must she include in her gross income?

What are several possible explanations for the markdown : What are several possible explanations for the markdown and slow sale of common waleth Edison's bonds?

Basis and diagonalization : Write the matrix of T in the standard basis of C^3. Find all eigenvalues of T. Is there a basis of C^3 such that the matrix of T in that basis is diagonal? If your answer is "NO", explain why.

Death of my father : What techniques for narration and/or description, outlined in your text, did you find in the essay on the death of my father by steve martin?

Probability that mean weight of men in sample is in range : Adult men have weights that are normally distributed with a mean of 172 lb and a standard deviation of 29 lb. Find the probability that the mean weight of the men in the sample is between 170 and 175 lb.

Business management : Business management

Loss from the transaction : Blue Company sold machinery for $45,000 on December 23, 2010. The machinery had been acquired on April 1, 2008, for $49,000 and its adjusted basis was $14,200. The § 1231 gain, § 1245 recapture gain, and § 1231 loss from this transaction are:

User Account

All Pages