The trace of a square matrix A, denoted tr A, is the sum of the elements on

Question:

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 sum of the squares of all entries of A.

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: 9780070985100

7th Edition

Authors: W. Keith Nicholson

See More Books

Question Posted: Jun 21, 2016 06:26 AM

See More Questions

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...
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 +...
Informative Speech Critique Evaluating Rhetorical Choices You may just number the questions and add a paragraph or two to answer - 1. Did you find the speaker credible? Why or why not? 2. Did the...
SAS No. 99 requires auditors to conduct a brainstorming session to discuss the potential for fraud and how the auditor might respond to the risk of fraud. However, the standard provides limited...
Correlation coefficients can help us understand how two variables are related. What are two variables that might have a strong positive correlation? A strong negative correlation? What might be two...
Be an effective team member
Dominick Corporation is authorized to issue 10,000 shares of $40 par value, 10% preferred stock and 200,000 shares of $5 par value common stock . On January 1, 2012, the ledger contained the...
Halifax Manufacturing allows its customers to return merchandise for any reason up to 90 days after delivery and recere a credit to their accounts. All of Halifax's sales are for credit (no cash is...
Assume high school coach Emily Williams has seven possible swimmers for a four-person relay team. a. If the order for the freestyle relay is unimportant, how many different relay teams are possible?...
Find a, b, a1, and b1 if: (a) (b) 2 a b 1 2 1 4
A square matrix P is called an idempotent if P2 = P. Show that: If P is an idempotent, so is Q = P + AP - PAP for any square matrix A (of the same size as P).
Effect of Constraints on Capital Investment Decisions: Lucitania Oil Company has limited investment funds. It has $1 million available for investment. The company must choose from among three...
Why the sudden increase in income before taxes in 2021? 8. Why were the operating assets the highest in 2019? 9. Why are the short-term loans the highest in 2020? 10. Why are the other long-term...
Mercy wants to make sure that she will be able to provide for her daughter's college and plans to open a savings account with a bank that is ready to pay interest as shown below per year compounded...
Question 1. For a firm that uses portfolio management, please give a real or hypothetical example of how the CEO's personal bases for power help organizational performance. Question 2. Give a real...
Make a schedule that you would use that effectively illustrates working with paraprofessionals that includes collaboration time. Use the examples provided in the following resources to guide your...
How does the integration of technology and automation influence employee motivation and job satisfaction within modern organizational contexts ?
Use the following data to estimate a value of K p at 1200 K for the reaction 2 H 2 (g) + O 2 (g) 2 H 2 O(g) C(graphite) + CO2(g) CO(g) + H(g) = C(graphite) + O(g) 1 2 2 CO(g) CO(g) + HO(g) CO(g) Kc...
For the given transfer function: Vo(s) / Vi(s) = (s^2C^2R^2 + 1) / (s^2C^2R^2 + 4sCR + 1) Assumiing that 1/(CR) = 120 PI so write the matlab code to find the magnitude plot
Let a be a fixed nonzero vector in R2. A mapping of the form L(x) = x + a is called a translation. Show that a translation is not a linear operator. Illustrate geometrically the effect of a...
Let L: R2 R2 be a linear operator. If L((1,2)T) = (-2,3)T and L((l,-1)T) = (5, 2)T determine the value of L((7, 5)T).
Let C be a fixed n x n matrix. Determine whether the following are linear operators on R n n (a) L(A)= CA + AC (b) L(A) = C2A (c) L(A) = A2C
Consider a 5 year debt with a 15% coupon rate paid semi-annually, redeemable at Php1,000 par. The bond is selling at 90%. The flotation cost is Php50 per bind. The firm's tax bracket is 30%.
A project will generate annual cash flows of $237,600 for each of the next three years, and a cash flow of $274,800 during the fourth year. The initial cost of the project is $749,600. What is the...
You want to invest annual amounts over the next 15 years. If your goal is to have $15,000 at the end of that time and if you can earn 8 percent on your invested funds, how much do you need to invest...

The trace of a square matrix A, denoted tr A, is the sum of the elements on

Question:

Step by Step Answer:

a If A aij then the trace of A is the sum of the entries on t...View the full answer

Linear Algebra With Applications

Students also viewed these Linear Algebra questions