A simple demonstration of the existence of the jordan canonical form for any square matrix

All the demonstrations known to this author of the existence of the Jordan Canonical Form are somewhat complex - usually invoking the use of new spaces, and what not. These demonstrations are usually too difficult for an average Mathematics student to understand how he or she can obtain the Jordan Canonical Form for any square matrix. The method here proposed not only demonstrates the existence of such forms but, additionally, shows how to find them in a step by step manner. I do not claim that the following demonstration is in any way “elegant” (by the standards of elegance in fashion nowadays among mathematicians) but merely simple (undergraduate students taking a fist course in Matrix Algebra would understand how it works).

A class of improved heteroskedasticity-consistent covariance matrix estimators

The heteroskedasticity-consistent covariance matrix estimator proposed by White (1980), also known as HC0, is commonly used in practical applications and is implemented into a number of statistical software. Cribari–Neto, Ferrari & Cordeiro (2000) have developed a bias-adjustment scheme that delivers bias-corrected White estimators. There are several variants of the original White estimator that also commonly used by practitioners. These include the HC1, HC2 and HC3 estimators, which have proven to have superior small-sample behavior relative to White’s estimator. This paper defines a general bias-correction mechamism that can be applied not only to White’s estimator, but to variants of this estimator as well, such as HC1, HC2 and HC3. Numerical evidence on the usefulness of the proposed corrections is also presented. Overall, the results favor the sequence of improved HC2 estimators.

The benefits and pitfalls of participating in a corporate inversion: a case study of two companies on two different paths

Even though the term corporate inversion has been heard globally for decades, it has only become more prevalent in the United States during the past two years. This case study examines two United States companies that recently had very high profile and public corporate inversion experiences. Complicated tax laws and high tax rales have long eroded the ability of United States companies to remain competitive on a global scale. During the past two years, tax reform has been elevated to the Presidential and Congressional levei. Because these reform efforts have stalled, however, and in the constant search for ways to become more competitive and profitable, United States dorniciled companies have begun to more aggressively explore corporate inversion. This case study of Walgreens Alliance Boots and Mylan N.V., is undertaken because while the reasons to pursue a corporate inversion for both companies were very similar and done during the same time period, the internai process and final outcome were dramatically different. The other dynamic studied is the role both internai and externai politics had on these two cornpanies and how they influenced the decisions made by the executives. Lastly, the Obama Administration continues to threaten so called "corporate America" to remain in the country through regulatory pressure, but this has not stopped companies frorn pursing corporate inversions. Legislatively, attempts at corporate tax reform, another way to encourage Untied States companies to remain, have also failed. I will not try to determine i f a corporate inversion is the right path for a company to take. I am examining how the rise o f the practice o f corporate inversions has been elevated in boardroorns, on Wall Street, in Congress and at the White House during the past two years.