The (*) columns of a matrix have this property if the matrix has a nonzero determinant.
Two solutions to homogeneous second order linear differential equations with this property have zeroes that alternate according to the Sturm separation theorem. Sets of the edges of a graph possess an analogous property to this one if they make up a forest; that generalization of this property is called a matroid. Reduction of order takes one solution to a differential equation and produces another solution with this property. The (*) columns of a matrix have this property if the matrix has a nonzero determinant. A set with this property that spans a vector space is said to be a basis for that space. For 10 points, name this property possessed by a family of vectors if no vector can be written as a linear combination of the others.
Two solutions to homogeneous second order linear differential equations with this property have zeroes that alternate according to the Sturm separation theorem.
linear {independence} [accept word forms]