There is an alternative criterion for positive definiteness based on subdeterminants of the matrix. The 2x2 version
Question:
(a) Prove that a 3 x 3 matrix
Is positive definite if and only if α > 0, ad - b2 > 0 det K > 0.
(b) Prove the general version: an n x n matrix K > 0 is positive definite if and only if all the upper left square k x k subdeterminants are positive for k = 1 ,........., n Hint: See Exercise 1.9.19
Transcribed Image Text:
abc
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 71% (7 reviews)
According to Exercise 1919 the pivots of a regular ...View the full answer
Answered By
Larlyu mosoti
I am a professional writer willing to do several tasks free from plagiarism, grammatical errors and submit them in time. I love to do academic writing and client satisfaction is my priority. I am skilled in writing formats APA, MLA, Chicago, and Harvard I am a statistics scientist and I can help out in analyzing your data. I am okay with SPSS, EVIEWS, MS excel, and STATA data analyzing tools.
Statistical techniques: I can do linear regression, time series analysis, logistic regression, and some basic statistical calculations like probability distributions. . I'm ready for your working projects!
Services I would offer:
• Academic writing.
• Article writing.
• Data entry.
• PDF conversion.
• Word conversion
• Proofreading.
• Rewriting.
• Data analyzing.
The best reason to hire me:
- Professional and Unique work in writing.
- 100% satisfaction Guaranteed
- within required time Express delivery
- My work is plagiarism Free
- Great communication
My passion is to write vibrantly with dedication. I am loyal and confident to give my support to every client. Because Client satisfaction is much more important to me than the payment amount. A healthy client-contractor relationship benefits in the longer term. Simply inbox me if you want clean work.
5.00+
3+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Linear Algebra questions
-
There is an alternative method for changing a base 10 numeral to a different base. This method will be used to convert 328 to base 5. Dividing 328 by 5 gives a quotient of 65 and a remainder of 3....
-
Analyze Example 15-9 based on the most probable criterion and determine the actions that are selected at each decision node. Do any actions differ from those selected in the example? Example 15-9 In...
-
Analyze Example 15-9 based on the expected profit criterion and determine the actions that are selected at each decision node. Do any actions differ from those selected in the example? Example 15-9...
-
Adrian Webb bought 618 bricks to build a barbecue pit, paying $185.40. Find the cost per brick. (HINT: Cost per brick means the cost for one brick.) The cost per brick is s (Round to nearest hundidth)
-
Fredericks Farm Factory (FFF) currently maintains an average inventory valued at $3,400,000. The company estimates its capital cost at 10 percent, its storage cost at 4.5 percent, and its risk cost...
-
According to the Digest of Educational Statistics, a certain group of preschool children under the age of one year each spends an average of 30.9 hours per week in nonparental care. A study of state...
-
In general, the creep compliances, \(S_{i j}(t)\) and the relaxation moduli, \(C_{i j}(t)\) are not related by a simple inverse relationship. Show that only when \(t ightarrow 0\) and when \(t...
-
A New Hampshire resort offers year-round activities: in winter, skiing and other cold-weather activities and, in summer, golf, tennis, and hiking. The resorts operating costs are essentially the same...
-
In the United States there will always be an inherent conflict between the criminal defendant's Sixth Amendment right to a fair trial and the media's First Amendment freedom of press rights. The...
-
Mr B aged 52 years, has earned rupees 75,00,000 out of his business. His ex-wife gifted him a car worth rupees 8 lakh. He spent a total of rupees 20 lakh during a family trip. He won a lottery of 16...
-
(a) Prove that any regular symmetric matrix can be decomposed as a linear combination K = d1,11IT1 + d2I21T2 + ¢ ¢ ¢ + dn11lT1 (3.69) of symmetric rank 1 matrices, as Exercise 1.8.15....
-
Let K be a symmetric matrix. Prove ha if a non- positive diagonal entry appears anywhere (not nece ssarily in the pivot position) in the matrix during Regular Gaussian Elimination. (hen K is not...
-
Use one of the scenarios in the previous exercise to practice facilitating and participating in a meeting. You may do this in person or online. Have each person assume the role of another...
-
In (a)-(d), state whether the equation is an identity (valid for all \(\mathbf{F}\) or \(f\) ). If it is not, provide an example in which the equation does not hold. (a) \(\operatorname{curl}(abla...
-
Refer to Exercise 10. The company has two positions open. They will interview candidates until two qualified candidates are found. Let \(Y\) be the number of candidates interviewed up to and...
-
What is the difference between feedback and feed-forward?
-
A radioactive mass emits particles according to a Poisson process. The probability that no particles will be emitted in a two-second period is 0.5 . a. What is the probability that no particles are...
-
How are combined fragments used in sequence diagrams?
-
The procedure for transferring information from a journal to ledger accounts is called a. Journalizing. b. Adjusting. c. File maintenance. d. Posting. e. None of these answers
-
The age-old saying for investing is "buy low and sell high," but this is easier said than done. Investors who panic about falling prices sell their investments, which in turn lowers the price and...
-
Find an upper triangular matrix that satisfies 3 1 30
-
Invent and prove a theorem that describes how to multiply two diagonal matrices.
-
(a) Make up a consistent linear system of five equations in five unknowns that has a lower triangular coefficient matrix with no zeros on or below the main diagonal. (b) Devise an efficient procedure...
-
Develop a simple application of two- variable linear programming problem to find an optimal product mix in a 'realistic' context. Specify the resources to be considered requirements, and the market...
-
According to the Google, Inc. Privacy Policy Litigation, on what date did Google announce their new universal privacy policy?
-
alcolm and Brianna were married on December 15, 2022. They spent the remainder of the tax year in Paris, France. Malcolm is a lifelong resident of North Carolina. Brianna was a lifelong resident of...
Study smarter with the SolutionInn App