Nontrivial solution意思

"Nontrivial solution" is a term used in mathematics, particularly in the context of solving equations or systems of equations. A trivial solution is a solution that is trivially obvious or that does not provide any meaningful information. In contrast, a nontrivial solution is a solution that is not trivial and provides meaningful information about the problem at hand.

For example, in the context of linear algebra, the trivial solution to a system of linear equations is the solution where all variables are zero. A nontrivial solution is any solution where at least one variable is non-zero.

The term can also be used in other branches of mathematics, such as abstract algebra, where a trivial solution might refer to the identity element of a group, and a nontrivial solution would be any other element of the group.