Let A be a diagonalizable n x n matrix. Prove that if B is any matrix that

Question:

Let A be a diagonalizable n x n matrix. Prove that if B is any matrix that is similar to A. then B is diagonalizable.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra with Applications

ISBN: 978-0131857858

7th edition

Authors: Steven J. Leon

See More Books

Question Posted: Jun 13, 2016 01:01 AM

See More Questions

Let A be a diagonalizable n n matrix with eigenvalues 1, 2, . . ., n(including multiplicities). Show that: (a) det A = 12 . . . n (b) trA = 1 + 2 + . . . + n
a. Let A be a diagonalizable n x n matrix. Show that if the multiplicity of an eigenvalue A is n, then A = A1. b. Use part (a) to show that the matrix A is not diagonalizable. 3 8
Let A be a diagonalizable matrix and let X be the diagonalizing matrix. Show that the column vectors of X that corresnd to nonzero cigenvalues of A form a basis for R(A.
Suppose the money supply is $250 million dollars and the demand for money is given by Qm D = 400 - 40i, where Qm D is in millions of dollars. A. What is the equilibrium interest rate in this economy?...
Red Tiger Company purchased packaging equipment on January 3, 2005, for $180,000. The equipment was expected to have a useful life of 3 years, or 22,320 operating hours, and a residual value of...
The U. S. Department of Transportation maintains statistics for mishandled bags per 1,000 airline passengers. In October 2013, Delta mishandled 1.55 bags per 1,000 passengers. What is the probability...
Explain why flight speeds below L/DMAX are not recommended.
You are considering the risk-return profile of two mutual funds for investment. The relatively risky fund promises an expected return of 8% with a standard deviation of 14%. The relatively less risky...
As a manager, how has research helped you manage people and projects? Explain with examples.
Entries into T accounts and Trial Balance Marjorie Knaus, an architect, organized Knaus Architects on January 1, 20Y4. During the month, Knaus Architects completed the following transactions: a....
Let x. y be nonzero sectors in Rn. n 2. and let A = xyT Show that (a) A = 0 is an eigenvalue of A with n - I linearly independent elgenvectors and consequently has multiplicity at least n - 1 (see...
Show that if A and B are two n x n matrices that both have the same diagonalizing matrix X. then AB = BA.
Show that Y1 is that linear combination of the original standardized data that has the most variance. That is, show that var(w1Z1 +w2Z2) is maximized (subject to the constraint w21 + w22 = 1) by the...
Write a Python program to: Read the amount of a purchase from the user Calculate the amount of GST Calculate the total with GST Print out a formatted sales receipt (example below) Your program should...
Dwayne just received his student loan statement that indicates that he has paid $3,500 of interest on his student loan during this tax year. What is the maximum amount of interest that he may deduct,...
Above you will find an interview I made with Holocaust survivor NormanFrajman. Norman lived through the Warsaw Ghetto uprising and more than two concentration camps during the Holocaust. In this...
Arco Steel, Inc. generated total sales of $53,294,714 during the fiscal year. Depreciation and amortization for the year totaled $2,216,971, and cost of goods sold was $26,454,794. Interest expense...
For this assignment you are required to pick a company that is publicly traded on one of the many US exchange floors. Go to the SEC "Edgar" database (...
Assess the value of the four-step procedure for analyzing transactions.
What is the shape of the exponential distribution?
Let f: Rn Rm be a matrix transformation defined by f(u) = Au, where A is an m x n matrix. Show that if u and v are vectors in Rn such that f(u) = 0 and f(v) = 0, where Then f(cu + dv) = 0 for any...
(a) Let O: Rn Rm be the matrix transformation defined by 0(u) = Ou, where O is the m n zero matrix. Show that O(u) = 0 for all u in Rn. (b) Let I: Rn Rn be the matrix transformation defined by...
F: R2 R2 is a counterclockwise rotation through 2 / 3 Ï radians; Sketch u and its image under each given matrix transformation f. 3
What is one specific security tactics to protect the network. Identify specific tools selections to accomplish compliance and audit requirement Describe how alerts would be collected and presented...
1. Solve each equation for x, where 0x & a) sin x-= 0 b) cosx-3 cosx+2=0
Explain Article III Standing, and explain how to achieve standing. b) Explain Negligence, and provide an example of a Negligence claim. c) What happened in the case of Genesco v. Visa? d) Explain the...

Let A be a diagonalizable n x n matrix. Prove that if B is any matrix that

Question:

Step by Step Answer:

If A is diagonalizable then A XDX 1 where D is a diag...View the full answer

Linear Algebra with Applications

Students also viewed these Linear Algebra questions