Article 148995 of alt.religion.kibology: Newsgroups: alt.sci.physics.new-theories,sci.physics.relativity,sci.physics,sci.math,alt.religion.kibology From: kibo@world.std.com (James "Kibo" Parry) Subject: Re: AM = I implies MA = I for matrices Sender: news@world.std.com (Mr Usenet Himself) X-Hello-To: Archimedes Plutonium Date: Mon, 22 Jun 1998 09:25:00 GMT X-Battlestar-Galactica-Date: 4721 centons, 63 microns, .02 rouettes Organization: welcome datacomp Followup-To: alt.religion.kibology In alt.sci.physics.new-theories, sci.physics.relativity, sci.physics, sci.math, Alexander Abian (abian@iastate.edu) wrote: > > (posted by request) Dear Dr. Alexander Abian, Could you please post a photo of your head in a microwave oven, to six or seven newsgroups by the end of the day? > In many books they define the inverse of a square matrix M to be a > matrix A provided AM = MA = I. Yes, but although MA may be I, MOM is WOW inverted! I dare you to walk around town with a T-shirt that says "MA = I". > There is no need for this since in matrices (say over real numbers) with toast points and a side of homemade peanut butter on a white celery stick. > AM = I implies MA = I where, of course I is the unit (square) matrix. > > You can prove this implication, without invoking the notions of the > characteristic polynomial or minimal polynomial for matrices. This can > be shown quite elementarily as follows. > > Without loss of generality let M be a 2 by 2 matrix over reals > such that > > (1) AM = I where I is the unit 2 by 2 matrix. > > We show that MA is also equal to I. > > Clearly M is a vector of a 4 dimensional vector space V whose basis > is given, say, by the following 4 two-by-two matrices > > 1 0 0 1 0 0 0 0 > ( ), ( ), ( ), ( ) > 0 0 0 0 1 0 0 1 Here, let me help you finish your clever new ASCII .signature: "BUD!" "WEIS!" "ER!" "TIMEHASINERTIA!" \ / / / 1 0 0 1 0 0 0 0 ( ), ( ), ( ), ( ) 0 0 0 0 1 0 0 1 I have named your four frogs "See No Evil", "Hear No Evil", "Croak No Evil", and "Evil Evil Evil". That way they still add up to the unit matrix frog. > since M, in an obvious way, is a linear combination of the above 4 matrices > over the real numbers. > > Now, consider in V the following 5 vectors > > M, M^2, M^3, M^4, M^5 > > Clearly, in view of (1) none of the above 5 matrices is equal to 0 > (the 2 by 2 zero matrix). For instance since by (1) A A A M M M = I > we see that M^3 cannot be 0, etc. > Hence the above 5 nonzero matrices are linearly dependent since V is > a four dimensional vector space. Thus, > > a M + b M^2 + v M^3 + d M^4 + e M^5 = 0 > > where not every real number a, b, c, d, e is equal to zero. Let, us say, > all are zero except b and e. So we have > > b M^2 + e M^5 = 0 which implies > > b A A A M M + e A A A M M M M M = O but then by (1) we have DR. ALEXANDER ABIAN: bAAAAAAAAAMMMM! eAAAAAMMMMMMMMMMM! bRRRRRRRZZZZTTTT! DR. CARL SAGAN: Look, Dr. Asimov, Dr. Abian's trying to tell us something. DR. ISAAC ASIMOV: What is it, Alex? Is something wrong with your experiment? Is the wine contaminated with psilocybin again? DR. ALEXANDER ABIAN: bAAAAAAAAAAAAAAAAAAAMMMMMMMM! wAAAAAAAAAAAAAAAAAHHHHHHH! DR. CARL SAGAN: Jinkies! You say the Moon's come out of orbit and is about to crush little Timmy? DR. ISAAC ASIMOV: Good boy! Take us to him, Alex! (They run off. Wild adventures ensue.) > b A + e M M = 0 or > > (2) A = (-e/b) M^2 But then obviously, by (1) and (2) we have > > I = AM = (-e/b) M^3 = M (-e/b) M^2 = MA = I, as desired. All my life I've wanted to live in a world where MA = I, and at last my dream has come true! HOORAY FOR ALEXANDER ABIAN FOR DISCOVERING THE bAAAAAAAAMMMM RAY! The next thing I desire is proof that Bob Hope is a member of the empty set. -- K. In theater they call it the limbo set. Article 149746 of alt.religion.kibology: Newsgroups: sci.math,alt.religion.kibology Path: utk.edu!cpk-news-feed4.bbnplanet.com!cpk-news-feed1.bbnplanet.com!cpk-news-hub1.bbnplanet.com!news.bbnplanet.com!news2.ais.net!jamie!ais.net!uunet!in3.uu.net!world!kibo From: kibo@world.std.com (James "Kibo" Parry) Subject: Re: PLEASE FILL IN THE DOTS Sender: news@world.std.com (Mr Usenet Himself) Message-ID: X-Hello-To: Archimedes Plutonium Date: Wed, 15 Jul 1998 01:41:10 GMT X-Battlestar-Galactica-Date: 8316 centons, 67 microns, .01 abians References: <6ogcqt$h5a$1@news.iastate.edu> Nntp-Posting-Host: ppp0a012.std.com Organization: welcome datacomp X-Newsreader: MT-NewsWatcher 2.4.4 Followup-To: alt.religion.kibology Lines: 118 Xref: utk.edu sci.math:231542 alt.religion.kibology:149746 In sci.math, Alexander Abian (abian@iastate.edu) wrote: > > (Recall that a function is Riemann integrable on [a, b] if and > only if it is bounded and continuous almost everywhere on [a, b]) > Please, fill in the dots in as simple and as nontrivial a way > as you can in the following 2 Theorems. I was wrong, there are worse birthday party games than the ones Don Saklad comes up with. And you're a day late too! I hate your parties! Give me all my presents and get out! Release the Time Bees! > > THEOREM 1. Let .................................................... > ..................................................................... > > ............................ Then for every x in [a, b] > > F(x) - F(a) = the Riemann integral from a to x of F' > > if and only if ............................................... > .............................................................. > All right, A.A., I'll have a go at that one. THEOREM 1. Let a whole bunch of dots come out of your pencil, don't inhale too deeply or the dots will go straight up your nose into your brain like happened to A.A.! Then for every x in [a, b] F(x) - F(a) = the Riemann integral from a to x of F' if and only if Alexander Abian could hit himself in the kisser with a huge cream pie made from cream of cinderblock, if only. It MUST be right 'cause it fits exactly. Science is like a jigsaw puzzle. But only real scientists are allowed to peek at the picture on the box. It even has blank lines in it for no reason just like the secret theorem! Will our next Mystery Theorm sign in please... > > THEOREM 2. Let ......................................................... > ......................................................................... > > ............................. Then for every x in [a, b]. > > > F(x) - F(a) = the Riemann integral from a to x of g > > if and only if ..................................................... > ..................................................................... > Vanna, I'd like to buy a perjorative. Is there a "wacko" in the puzzle? THEOREM 2. Let ......................................................... ......................................................................... ............................. Then for every x in [a, b]. F(x) - F(a) = the Riemann integral from a to x of g if and only if ..................................................... ..................................................................... THEOREM 2. Let 's pretend Dr. Alexander Abian is not a full-blown wacko. This would mean "TIME HAS INERTIA" is true some of the time, but at other times it's "TIME HAS COOTIES" Then for every x in [a, b]. F(x) - F(a) = the Riemann integral from a to x of g if and only if TIME HAS INERTIA while ABIAN HAS COOTIES. Because if TIME HAS COOTIES then ABIAN HAS INERTIA, as his staying power proves. Ha! I have proven my theorem, a corrolary of which is that nobody else will ever be able to prove anything ever again because my theorem is so perfect that it used up all the truth value everywhere in the Universe! Yes, the recent inflation of truth values was all my fault, but it's too late now, because everything I say will be true from now on due to this mistake in the laws of quantum physics. If I say that the sky is a baboon made from crumpled aluminum foil, it will be true! If I say that NBC's "seaQuest DSV" is William Shakespeare's masterpiece, it will be true! And if I continue to insinuate that Alexander Abian just MIGHT be a wacko, it will of course STILL be true! > -- > > -------------------------------------------------------------------------- > > ABIAN TIME-MASS EQUIVALENCE FORMULA T = A m^2 in Abian units > ALTER EARTH'S ORBIT AND TILT - STOP GLOBAL DISASTERS AND EPIDEMICS > ALTER THE SOLAR SYSTEM. REORBIT VENUS INTO A NEAR EARTH-LIKE ORBIT > TO CREATE A BORN AGAIN EARTH (1990) ABIAN TIME-LIFE SUBSCRIPTION OFFER "RADIOS OF THE MIDDLE AGES" ALTER ABIAN'S HAIRPIECE AND PART - STOP COWLICKS AND COMB-OVERS ALTER YOUR CAT TO CONTROL THE PET POPULATION. REORBIT BOB BARKER TO WIN A BRAND NEW BORN AGAIN CAR ($19990) I will not stoop to mocking your asymmetric row of stupid hyphens. -- K. (revolving head of Michael York) TIME HAS NOOOO SANCTUAAARRRYYYYY