Linear independence (functions): Difference between revisions
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(Created page with "Category:Differential Equations Given a set of functions <math> \vec{x}^{(1)},\ldots,\vec{x}^{(k)} </math> Defined in a < t < b. They are linearly independent of the only solution to <math> c_1\vec{x}^{(1)}+\ldots+c_k\vec{x}^{(k)}=0 </math> is all c's being 0.") |
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Similar to the [[Wronskian]], as long as it is independent when evaluated at one t, it is sufficient to say that the set is independent. | |||
Latest revision as of 14:28, 10 June 2024
Given a set of functions
Defined in a < t < b. They are linearly independent of the only solution to
is all c's being 0.
Similar to the Wronskian, as long as it is independent when evaluated at one t, it is sufficient to say that the set is independent.
