Grammian determinant

The Grammian determinant provides a necessary and sufficient method of determining whether a set of continuous functionsMathworldPlanetmathPlanetmath f1,f2,,fn is linearly independentMathworldPlanetmath on an interval I=[a,b] with respect to the inner productMathworldPlanetmath


It is defined as:


If the functions are continuous on I, then G=0 if and only if the set of functions is linearly dependent. Note that the Grammian determinant is a special case of the more general Gram determinantMathworldPlanetmath.

Title Grammian determinant
Canonical name GrammianDeterminant
Date of creation 2013-03-22 17:37:33
Last modified on 2013-03-22 17:37:33
Owner slider142 (78)
Last modified by slider142 (78)
Numerical id 6
Author slider142 (78)
Entry type Definition
Classification msc 34A12
Related topic WronskianDeterminant
Related topic GramDeterminant