examples of non-commutative operations

A standard example of a non-commutative operation is matrix multiplicationMathworldPlanetmath. Consider the following two integer matrices:


If we compute AB we get


but if we compute BA we have


Since ABBA we conclude that matrix product is not commutativePlanetmathPlanetmathPlanetmath.

Operations do not necessarily have to operate on numbers. Another classic example is function composition. Let f and g be real functions given by


We see that




Since we got different functionsMathworldPlanetmath, we conclude that function composition is not commutative.

Title examples of non-commutative operations
Canonical name ExamplesOfNoncommutativeOperations
Date of creation 2013-03-22 15:03:04
Last modified on 2013-03-22 15:03:04
Owner yark (2760)
Last modified by yark (2760)
Numerical id 10
Author yark (2760)
Entry type Example
Classification msc 20-00