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Matrices are considered very important in mathematics. What are some examples of applications of matrices to real world problems that would be understandable by a layman?

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Have you looked at the Wikipedia article? –  T. Bongers Nov 6 '13 at 6:35
    
The link given by T.Bongers coyly talks about text mining. I would say that every time you use Google, a huge matrix is involved. And that's one of IMHO least interesting applications of matrices. –  Jyrki Lahtonen Nov 6 '13 at 7:03
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If you have system of nonlinear equations and linearize them, you get a linear system, which can be represented by a matrix.

So, matrices are relevant whenever you can model the real world with equations, which is very often.

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One would be hard pressed to find a tool in mathematics that is more widely used for real world applications than matrices and linear algebra.

  • Physicists and engineers to model physical systems and perform precision calculations needed for complex machinery to work. Electronics networks, airplane and spacecraft, and chemical manufacturing all require fine tuned computations arising from matrix transformations.

  • Routing problems and other problems in operations research make extensive use of very large matrices. There are entire subfields of this discipline related to finding the fastest, most accurate solutions to various matrix problems, for purposes of managing very large supply chains.

  • Many internet and computer programming companies also use matrices as data structures to track user information, perform search queries, and manage databases. In the world of information security, many public key cryptosystems are designed to work with matrices over finite fields, in particular those which are designed with speed of decryption as a goal.

These are only a few examples, but let me assure you that nearly any quantitative line of work will make extensive use of matrix equations.

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yeah. i can find the usage in terms of equations, but i want the generic use of the matrix if used any where, be it even of small usage. –  Saurabh Nov 6 '13 at 8:16
    
@Saurabh What exactly do you mean by a "generic use"? –  D. Ansuerze Nov 6 '13 at 21:21
    
generic use in the sense we use additions for calculating our cash, counting the people in a queue. The same way use of matrix for a common man.-@D.Ansuerze –  Saurabh Nov 7 '13 at 7:30
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