How is matrix multiplication useful?

Question

What are the uses for matrix multiplication other than for homework exercises?

Answer 1

There are many uses in science and engineering. I worked on a DSL project. The electronic circuitry is modeled by differential equations. A computer program that uses matrix operations was able to get the circuit to work.

Answer 2

Aside from the very good general answers given already, it can be added that the Stress Tensor provides a very important use of matrices and matrix multiplication. The stress tensor is a way of mathematically expressing the state of stress at a point in a solid medium.
Matrices are also used to express the conservation equations, mass, energy and momentum at each point of a fluid, for example, in modeling how the fluid will move within its boundary under applied forces and pressures. Manipulating the matrices then yields the solution ... the strain in a solid medium, or the velocity distribution and other properties in a fluid medium. It gets interesting.

Answer 3

Probably the one most often used is in the solution of families of linear equations. A 'matrix' can be thought of as a linear transform between vector spaces (or a homomorphism over a single vector space). In addition to which there are lots of things that you haven't as yet learned about matrices, such as how to use them to solve arbitrary systems of linear equations, how to find eigenvectors and eigenvalues (which are very important in physics and engineering), and a whole bunch of other stuff that you'll get to eventually. Trust me. But first, you gotta learn all about their arithmetic.

HTH ☺

Doug

Answer 4

Anytime anyone plays any 3D computer games is making use of matrix multiplications at an astounding rate and sophisication. 3D graphics modelling DEPENDS on them, it's the lifeblood of all 3D computer animation work.

Answer 5

One of the most common uses is to find cross product of vectors, something that you do everyday in physics.