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vector-valued solution

A solution to a system, written as a vector of functions rather than one function.

A vector-valued solution of \mathbf{x}'=A\mathbf{x} is a vector function \mathbf{x}(t)=(x_1(t),\ldots,x_n(t)) satisfying the system at every t; linear independence of several such solutions is tested with the vector Wronskian, the determinant of the matrix formed from them.

See also

system of first-order equations fundamental matrix
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