Question: How many orthononnal eigenvector bases does a symmetric n n matrix have?

How many orthononnal eigenvector bases does a symmetric n × n matrix have?

Step by Step Solution

★★★★★

3.40 Rating (169 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

If all eigenvalues are distinct there are 2n different bases ... View full answer

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

Document Format (1 attachment)

Word file Icon

952-M-L-A-E (2688).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Find the eigenvalues and an orthonormal eigenvector basis for the following symmetric matrices: (a) (b) (c) (d) (e) 7 2 3 3 (3 3) 2 -1 -1 5 431 013 104 461

Q:

A complex matrix A is called normal if it commutes with its Hermitian transpose: AA = AAT. (a) Show that every real symmetric matrix is normal. (b) Show that every unitary matrix is normal. (c) Show...

Q:

Let A be a 4 4 real symmetric matrix with eigenvalues 1 = 1, 2 = 3 = 4 = 0 (a) Explain why the multiple eigenvalue = 0 must have three linearly independent eigenvectors x2, x3, x4. (b) Let x1 be an...

Q:

Let u1,...,un be an orthonormal basis of Rn. Prove that it forms an eigenvector basis for some symmetric n n matrix A. Can you characterize all such matrices?

Q:

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...

Q:

Problem #5: Let A and B be n x n matrices. Which of the following statements are always true? (i) If det(A) = det(B) then det(A B) =0. (ii) If A and B are symmetric, then the matrix AB is also...

Q:

Suppose H is a symmetric n x n matrix. We consider the problem of computing an eigenpair of H. (a) Show that if v is an eigenvector of H with unit norm, and u is its corresponding eigenvalue, then...

Q:

5.1 please only write on paper. no explanation needed. Questions: 28, 33, 35 on paper 300 CHAPTER 5 Eigenvalues and Eigenvectors 26. The eigenvectors that we have been studying are sometimes called...

Q:

Please help me find the answers Exercise 7.5.2: Evaluating compositions. Let Ti : R3 - R3, T2 : R' _ R3, and T3 : R -> R' be linear transformations defined as follows. 1+2 T1 2+3 T2 = 21 - $2 T3 2 C1...

Q:

Problem #1: Find the values of a, b, and so that det(A) = ax? + bx +c. x -2 0 A=1|-2 x 2 3 -6 -4 Problem #1: : separate your answers with a comma | Just Save ' | Submit Problem #1 for Grading Problem...

Q:

Betty Ltd has an item of heavy machinery with the following details: Cost Accumulated depreciation Fair value Betty Ltd uses the revaluation model for all items of PP&E. What should Betty Ltd do...

Q:

1. The primary purpose of the basic economic order quantity model shown below is to calculate the reorder point, so that replenishments take place at the proper time to minimize the sum of carrying...

Q:

Determine the missing amounts for these independent situations Determine the missing amounts for these three independent situations. Total Direct Direct Manufacturing Manufacturing Materials Used...

Q:

Comment on the following 1955 quote from C. R. McConnell: The entire question of advocacy versus analysis in economics may be a variation of the resource allocation problem. It is reasonable to...

Q:

y: Games won (per 14 game season) x1: Rushing yards (season) x2: Passing yards (season) x3: Punting yards (yds/punt) x4: Field goal percentage (Field goals made/Field goals attemptedseason) x5:...

Q:

The electric power consumed each month by a chemical plant is thought to be related to the average ambient temperature (x1), the number of days in the month (x2), the average product purity (x3), and...

Q:

A study was performed on wear of a bearing y and its relationship to x1 = oil viscosity and x2 = load. The following data were obtained. (a) Fit a multiple linear regression model to these data. (b)...

Q:

Orange Corporation has just made a French Euro bid on a project located in France. It won't find out for 90 days whether it has won the contract. There will be a 15% signing bonus payable to the...

Q:

( Related to Checkpoint 9 . 2 and Checkpoint 9 . 3 ) ( Bond valuation relationships ) The 1 4 - year, $ 1 , 0 0 0 par value bonds of Waco Industries pay 6 percent interest annually. The market price...

Q:

Consider the following table: Stock Fund Bond Fund Scenario Probability Rate of Return Rate of Return Severe recession 0.10 34% 10% Mild recession 0.20 18% 6% Normal growth 0.45 14% 7% Boom 0.25 24%...