Thursday, April 22, 2010

~ Math Mood

Asalam alaikum,

Its raining cats & dogs here..
And while people are fancying to eat pakoras.. i'm getting an all math-mood.

Every once in a while, i feel like touching mathly subjects of interest to me.. even if it sounds or smells like blaah to anyone among my regular readers..
n I wonder why but lately this word blaah reminds me of;


cool expression.. eh?

Here are few things you didn't know about linear algebra..
[excuse me if you did already]
  1. The heart of Google is an enormous linear algebra problem. PageRank is essentially an eigenvalue problem.
  2. Many practical problems — optimization, differential equations, signal processing, etc. — boil down to solving linear systems, even when the original problems are non-linear.
  3. Practical applications often require solving enormous systems of equations, millions or even billions of variables.
  4. A system of a million equations can sometimes be solved on an ordinary PC in under a millisecond, depending on the structure of the equations.
  5. Iterative methods, methods that in theory require an infinite number of steps to solve a problem, are often faster and more accurate than direct methods, methods that in theory produce an exact answer in a finite number of steps.
  6. There are many theorems bounding the error in solutions produced on real computers. That is, the theorems don’t just bound the error from hypothetical calculations carried out in exact arithmetic but bound the error from arithmetic as carried out in floating point arithmetic on computer hardware.
  7. There is remarkably mature software for numerical linear algebra. People have worked on this software for many years.



And if you're interested enough in the subject, then surely you'll find these suggested reads beneficial -

Linear algebra book - easy to read and has a good mix of theory and application.
Applied Numerical Linear Algebra - that is if you want to jump into numerical linear algebra, at all.
Matrix Calculations - classic.

And this video too;

Watch it on Academic Earth
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