Wronski determinant | Wronskian determinant

The Wronskian of a set of n functions ϕ_1, ϕ_2, ... is defined by W(ϕ_1, ..., ϕ_n) congruent left bracketing bar ϕ_1 | ϕ_2 | ... | ϕ_n ϕ_1^, | ϕ_2^, | ... | ϕ_n^, ⋮ | ⋮ | ⋱ | ⋮ ϕ_1^(n - 1) | ϕ_2^(n - 1) | ... | ϕ_n^(n - 1) right bracketing bar . If the Wronskian is nonzero in some region, the functions ϕ_i are linearly independent. If W = 0 over some range, the functions are linearly dependent somewhere in the range.

Abel's differential equation identity | Gram determinant | Hessian | Jacobian | linearly dependent functions