The trace of a square matrix A is the sum of the diagonal entries in A and

Question:

The trace of a square matrix A is the sum of the diagonal entries in A and is denoted by tr A. It can be verified that tr(FG) = tr(GF) for any two n x n matrices F and G. Show that if
A and B are similar, then tr A = tr B.

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

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra and Its Applications

ISBN: 978-0321791542

4th edition

Authors: David C. Lay

See More Books

Question Posted: May 02, 2016 12:07 PM

See More Questions

The trace of a square matrix A, denoted tr A, is the sum of the elements on the main diagonal of A. Show that, if A and B are n n matrices: (a) tr(kA) = k tr(A) for any number k. (b) tr(AAT) is the...
The trace of a square matrix is the sum of the entries on its diagonal (its significance appears in Chapter Five). Show that Tr(GH) = Tr(HG).
The trace of a square matrix is the sum of the entries on the main diagonal (the 1, 1 entry plus the 2, 2 entry, etc., we will see the significance of the trace in Chapter Five). Show that trace(H +...
Population increase in northern Virginia requires new road constructions and repairs annually from 2022. More public schools will also be needed by 2035. The state of Virginia is considering an...
Suppose that 47% of all Americans have flown in an airplane at least once and that 28% of all Americans have ridden on a train at least once.What is the probability that a randomly selected American...
In some cases, a manager can engage in transactions that improve the appearance of financial reports without affecting the underlying economic reality. In this chapter, we discussed the importance of...
Reducing hand stress with patient transfer devices. Professional caregivers suffer from a high prevalence of muscle stress when transferring patients. Are commercially available friction-reducing...
As noted in Problem 5.3, microwave ovens operate by rapidly aligning and reversing water molecules within the food, resulting in volumetric energy generation and, in turn, cooking of the food. When...
When property is acquired in an exchange for non-like-kind property, the property received generally is valued at which of the following? A The adjusted basis of the property relinquished B The...
In this module you will apply attribute sampling to Brony's Bikes' prenumbered sales invoices to evaluate whether sales have been processed properly. Recall from Module II that several deficiencies...
Let D = {d1, d2} and B = {b1, b2} be bases for vector spaces V and W, respectively. Let T: V W be a linear transformation with the property that Find the matrix for T relative to D and B. T(di) = 3b1...
It can be shown that the trace of a matrix A equals the sum of the eigenvalues of A. Verify this statement for the case when A is diagonalizable.
Video Collaboration Studios (VCS) is continually growing new studios globally. The immersive environment created by VCS allows employees to connect face to face from any part of the world as if they...
The Log Jamboree amusement park ride at Six Flags over Georgia consists of an approximately rectangular flume that is 6 ft wide and is constructed from fiberglass (ks = 0.002 in). In the low-velocity...
57'-8" 1. The building perimeter walls are 1'2" thick and the interior walls are 1'0" thick. Fig 1 and Fig 2 detail the linear feet of 1'2" -thick foundation walls. In addition, side B is 8'4" tall...
The Orpheus Chamber Orchestra is celebrating its 50 years as an orchestra this year. Read the following articles about its unique structure: The first Charlotte article is copied below, the rest just...
Which of the five strategies for adapting products and promotion for global markets does Monster Employ? 15-16. Which factors in the global marketing environment have challenged Monster's global...
Analysis of Current International Economic Environment in Switzerland 1. Develop a lead sentence for this section that introduces the key subsections 2. Economic Environment describe Switzerland...
In Problems 4958, determine whether the given set is finite or infinite. Consider the set N of positive integers to be the universal set, and let E P H = {ne N T = {ne N E = {ne N P = {n e N n >...
1. Firms may hold financial assets to earn returns. How the firm would classify financial assets? What treatment will such financial assets get in the financial statements in accordance with US GAAP...
V is a nonzero finite-dimensional vector space, and the vectors listed belong to V. Justify each answer. (T/F) If p 2 and dim V = p, then every set of p - 1 nonzero vectors is linearly independent.
Show that the space C(R) of all continuous functions defined on the real line is an infinite-dimensional space.
Describe an infinite linearly independent subset of the subspace W in Exercise 29. Does this establish that W is infinite dimensional? Justify your answer. Data from in Exercise 29 Let A typical...
The tolal landed coet with the order gaantly sire of 6,000 unts is 4 (Enter your response roundod to the nearest dolar)
Boyne Inc. had beginning inventory of $12,000 at cost and $20,000 at retail. Net purchases were $120,000 at cost and $170,000 at retail. Net markups were $10,000, net markdowns were $7,000, and sales...
Apple inc. CONDENSED CONSOLIDATED BALANCE SHEETS (Unaudited) (In milions, except number of shares which are reflected in thousands and par value) LABILITES AND SHAREHOLDERS' EQUITY: Current...

The trace of a square matrix A is the sum of the diagonal entries in A and

Question:

Step by Step Answer:

If If B is diagonal then the diagonal entries of ...View the full answer

Linear Algebra and Its Applications

Students also viewed these Linear Algebra questions