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W(\phi_1, \ldots, \phi_n) \equiv \left\vert\matrix{
\phi_1 ...
...& {\phi_2}^{(n-1)} & \cdots & {\phi_n}^{(n-1)}\cr}\right\vert.

If the Wronskian is Nonzero in some region, the functions $\phi_i$ are Linearly Independent. If $W=0$ over some range, the functions are linearly dependent somewhere in the range.

See also Abel's Identity, Gram Determinant, Linearly Dependent Functions


Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 524-525, 1953.

© 1996-9 Eric W. Weisstein