Question: If A and B are orthogonally diagonalizable and AB = BA, show that AB is orthogonally diagonalizable.

If A and B are orthogonally diagonalizable and AB = BA, show that AB is orthogonally diagonalizable.

Step by Step Solution

★★★★★

3.41 Rating (157 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

By Exercise 36 in Section ... 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 (2 attachments)

PDF file Icon

1623_606b0df172ac5_699408.pdf

180 KBs PDF File

Word file Icon

1623_606b0df172ac5_699408.docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

If A is an invertible matrix that is orthogonally diagonalizable, show that A-1 is orthogonally diagonalizable.

Q:

A matrix A is orthogonally diagonalizable if there is an orthogonal matrix P that diagonalizes it. Show that the matrix is orthogonally diagonalizable. Synunetric matrices have orthogonal...

Q:

Assume that A and B are orthogonally similar (Exercise 12). Show that A and B are orthogonally similar.

Q:

Can you please help me prove the following questions? 4. Prove that every n X n matrix A with real eigenvalues is orthogonally similar to a lower triangular matrix T. 5. Prove or disprove each...

Q:

QUESTION 2 Given matrix A below, -2 3 0 -20 0 3 4 a- (6 pts.) What are the eigenvalues of A? b- (6 pts.) What are the eigenspaces corresponding to each eigenvalue? c- (6 pts.) What are the basis...

Q:

Let A and B be orthogonally diagonalizable n ( n matrices and let c be a scalar. Use the Spectral Theorem to prove that the following matrices are orthogonally diagonalizable: (a) A + B (b) cA (c) A2

Q:

2. [H] Suppose A and B are matrices such that both AB and BA are defined. a) Show that AB and BA are both square matrices. b) If AB = BA, show that 4 and B are both square and of the same size. ) If...

Q:

This problem is about matrix operation. In class, I presented the Strassen's algorithm for multiplying two square matrices. Now, we consider a special case of multiplying two square matrices: given...

Q:

Hello, I need the answer to this question please. 1. (30 pts) For all the calculations and proofs you are required to do, state clearly the properties (if any) and laws (if any) used. Note that parts...

Q:

Problem 1. Assume that a is any scalar, and that A, B, and C are matrices of sizes such that the indicated matrix products are defined. Prove the following:1 (i) (associativity) A(BC) = (AB)C. (ii)...

Q:

A packaging system ills boxes to an average weight of 18 ounces with a standard deviation of 0.2 ounce. It is reasonable to assume that the weights are normally distributed. Calculate the 1st, 2nd,...

Q:

Given the following planar block slide data: MohrCoulomb failure criterion applies 1 slope height H = 613 ft (187.8 m); 2 failure surface angle = 34 ; 3 slope angle =? ; 4 friction angle = 30 ;...

Q:

If CFFA = $ 2 0 ; CFTC = $ 1 5 ; and dividends paid = $ 1 0 , then the firm would have repurchased stock in the amount of $ 5 . True False

Q:

3. On a multiple VI 50-sec VR 50 schedule, we are likely to find a high rate of response on the (VI/VR/both) component(s).

Q:

Use the same approach as in Problem 9.27 to test whether the adjusted carbon monoxide (CO) level is related to the number of days abstinent from smoking?

Q:

Why are nonparametric methods well suited to a study of risk factors for smoking cessation?

Q:

Use nonparametric methods to assess whether treatment with captopril is effective in reducing urinary protein? Renal Disease Refer to the urinary-protein data in Table 8.16 (p. 324). Table 9.16:...

Q:

solve.............. The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.9 days and a standard deviation of 1.6 days. What is the median recovery...

Q:

Please show all steps and double check your work! Question 9 1 pts A $1000 par, semiannual-pay bond has a current price of $1,058 has a modified duration of 6.19. What is the dollar value of an 01?...

Q:

Question 4 ( 1 5 pts ) . Glucose ( C 6 H 1 2 O 6 ) in the grain is converted into ethanol ( C 2 H 5 O H ) and propenoic acid ( C 2 H 3 C O 2 H ) during the fermentation of grain by the following...