O'Reilly logo

Physical Mathematics by Kevin Cahill

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

6.22 Wronski’s determinant

If the N functions y1(x), . . . , yN(x) are linearly dependent, then by (6.8) there is a set of coefficients k1, . . . , kN, not all zero, such that the sum

image

(6.202)

vanishes for all x. Differentiating i times, we get

image

(6.203)

for all x. So if we use the yj and their derivatives to define the matrix

image

(6.204)

then we may express the linear dependence (6.202) and (6.203) of the functions y1, . ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required