Linear Algebra Applications

ublinina2

Can anybody give me a few everday applications of Linear Algebra?

Son Goku

Depends on what you mean by everyday.
If you mean "everyday" in the sense of what the average person might use it for, then I'd say none.

If you mean which technologies require linear algebra to design or to run, then there are thousands.

vallo

Linear algebra is pretty broad ... could you be more specific?

Michael Collins

It would be used extensively in Communication Theory - i.e. designing communication systems. Also used in general signal analysis e.g. Fourier Transform.

Economics

Webmonkey

Engineering? Matrices used for solving huge simulatanous equations?

Son Goku

Sure actually Quantum Mechanics is just linear algebra, basically.

Farouk.Bulsara

ublinina2 wrote:

Can anybody give me a few everday applications of Linear Algebra?

Scientific models of the universe are often stated in terms of differential equations - e.g. Newton's Laws of Motion, Maxwell's Equations, etc.

Lots of science and engineering problems from the "real" world are derived from differential equations. These equations model both static and dynamic phenomena, such as stress/strain, heat flow, fluid flow, flow of electrons (electrical current), etc.

Computer models to solve differential equations normally involve (a) using a simplified version of the original equations and (b) a grid in space and/or time where the simplified equations are required to be solved. If we are solving Poisson's Equation on a square plate, we might have 1000 grid points in the x and y axes. This results in 1,000,000 simplified equations to solve. If we are dealing with a straightforward case, the equations are linear, so the solution is like solving Ax = b, where A is a matrix and x and b are vectors.

If there are nonlinearities in the simplified equation, then the system is linearized using something like Newton's method, which again requires the solution of a large linear system like Ax = b.

In either case, we are reduced to solving large linear systems like Ax = b, where the matrix A might have 1,000,000 rows and 1,000,000 columns.

The original problem might be something like weather forecasting, climate modelling, aerodynamic simulation, crash analysis of cars, etc, but the computer model is the same - solving large systems of linear equations - and this is a real-life, everyday and important application of linear algebra.

Fred

rjt

Some slightly more diverse applications: balancing chemical equations and finding unknown currents in circuits (see 'Contemporary Linear Algebra' - Anton & Busby). Also, there's a version of 'Elementary Linear Algebra' (also Anton; that guy seems to write everything :P) that includes a section on applications (with Forest Management, Genetics, Demographics and "Harvesting of Animal Populations" being the most unusual).