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| » Title: | The Probability That A Matrix Of Integers Is Diagonalizable |
| » Abstract: | The presenters investigate the question of the probability that a randomly chosen n by n matrix over the integers is diagonalizable. Such a probability is couched in terms of a variant on "natural density." Specifically, let n and k be positive integers, A(n,k) the number of diagonalizable n by n matrices over the integers with entries in the interval [-k,k], and B(n,k) the number of n by n matrices over the integers with entries in the interval [k,k]. Then, for fixed n, the presenters consider the value of A(n,k) / B(n,k) as k goes to infinity. To this end, they examine a (more computationaly amenable) lower bound on this probability by studying the number of n by n matrices over the integers in the interval [-k,k] that have n distinct eigenvalues. |
| This paper is also published in The American Mathematical Monthly's June/July 2007 issue (Vol.114 #6). * Online access requires MAA membership | |
My Google App Engine scribble wall: http://liew.appspot.com (Update: Google sign-in now *required*—you can thank the spammers)
I developed an application code-named Lexi-Rep (Lexical Reputation) used internally by security researchers at the Websense Security Labs. My research was demo'd by my CTO at a closed door security summit on the Yahoo campus. Read more here: http://www.darkreading.com/document.asp?doc_id=147581&f_src=darkreading_gnews
List of people, and some links to articles that captures slices of what I like about them.
Jacques Brel (April 8, 1929 - October 9, 1978)
George Eastman (July 12, 1854 - March 14, 1932)
Randy Pausch (October 23, 1960 - July 25, 2008)
I'm an ENTJ!
From Wikipedia: ENTJ (Extraversion, iNtuition, Thinking, Judging) is an acronym used in the Myers-Briggs Type Indicator (MBTI) publications to refer to one of the sixteen personality types.
ENTJs often excel in business. They are assertive, outspoken, confident, outgoing, energetic, charismatic, fair-minded, and unaffected by conflict or criticism. However, other traits may lessen the impact of their strengths. They may appear argumentative, confrontational, insensitive, intimidating, and controlling. They can overwhelm others with their energy, intelligence, and desire to order the world around them.
Genius is one percent inspiration and ninety-nine percent perspiration.
— Thomas Edison
You can have anything you want if you want it badly enough. You can be anything you want to be, do anything you set out to accomplish if you hold to that desire with singleness of purpose.
— Abraham Lincoln
As long as you're going to think anyway, think big.
— Donald Trump
The best way to have an edge is to live on one.
— Donald Trump
Only those who dare to fail greatly can ever achieve greatly
— Robert Kennedy
Cowardice asks the question, 'Is it safe?' Expediency asks the question, 'Is it politic?' Vanity asks the question, 'Is it popular?' But, conscience asks the question, 'Is it right?' And there comes a time when one must take a position that is neither safe, nor politic, nor popular, but one must take it because one's conscience tells one that it is right.
— Martin Luther King Jr.
Illegitimis non carborundum. That's Latin for: Don't let the bastards grind you down.
— Gen. Joseph Stilwell
Life is either a daring adventure or nothing.
— Helen Keller
I know of no more encouraging fact than the unquestionable ability of man to elevate his life by conscious endeavor.
— Henry David Thoreau
There's no substitute for hard work. If you work hard and prepare yourself, you might get beat, but you'll never lose
— Nancy Lieberman-Cline
It is not the critic who counts, not the man who points out how the strong man stumbled, or where the doer of deeds could have done better. The credit belongs to the man who is actually in the arena, whose face is marred by dust and sweat and blood, who strives valiantly, who errs and comes short again and again, who knows the great enthusiasms, the great devotions, and spends himself in a worthy cause, who at best knows achievement and who at the worst if he fails at least fails while daring greatly so that his place shall never be with those cold and timid souls who know neither victory nor defeat.
— Theodore Roosevelt, from a speech given in Paris at the Sorbonne in 1910
You can give up, sure, but the truth is that when you give
up, you have to live with that fact for the rest of your life. For me,
living with having given up in tough times is a much worse fate than
certain failure. If you fail, then by definition you have tried. But if you give up, you didn't.
— Jason Calacanis (article from Silicon Alley Insider)
There's a difference between interest and commitment. When you're interested in doing something, you do it only when circumstance permit. When you're committed to something, you accept no excuses, just results.
— Art Turock
A lot of geeks are pale, bespectacled, wear dark clothing and don't get out much - the stereotype exists because it is very often true. I could pass for a non-geek but it would be inaccurate. As you get into your late twenties and thirties you get into the era of 'the revenge of the geek'. Geeks run the world. Condoleeza Rice is a geek, Bill Gates is clearly a geek, many of the big filmmakers and writers are geeks, lots of military people are geeks. Anyone who has heard Donald Rumsfeld talk about military hardware knows they are in the presence of a geek. Geeks use their powers for good and for evil.
—
China Mieville
Greatness is never a given. It must be earned. Our journey has never been one of shortcuts or settling for less. It has not been the path for the
faint-hearted — for those who prefer leisure over work, or seek only the pleasures of riches and fame. Rather, it has been the risk-takers, the doers, the makers things of things — some celebrated but more often men and women obscure in their labor, who have carried us up the long, rugged path towards prosperity freedom.
—
Barack Obama
Trying seems to be a start for getting things done. You get to know the right way by doing it wrong
— Barbara Pack
It doesn't matter how many people don't get it. What matters is how many people do.
— Tim Ferriss
Robustness is when you care more about the few who like your work than the multitude who hates it (artists); fragility is when you care more about the few who hate your work than the multitude who loves it (politicians).
— Nassim Nicholas Taleb via Tim Ferriss
Freedom is just another word for entrepreneurship
You know what? Fuck beauty contests. Life is one fucking beauty contest after another. School, then college, then work... Fuck that. And fuck the Air Force Academy. If I want to fly, I'll find a way to fly. You do what you love, and fuck the rest.
— Little Miss Sunshine
Every man dies, but not every man truly lives
— William Wallace
Make hay while the sun shines