Rice at 14:28, 10 June 2024

2024-06-10T14:28:36Z

← Older revision		Revision as of 14:28, 10 June 2024
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	is all c's being 0.		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.

Rice: Created page with "Category:Differential Equations Given a set of functions $\vec{x}^{(1)},\ldots,\vec{x}^{(k)}$ Defined in a < t < b. They are linearly independent of the only solution to $c_1\vec{x}^{(1)}+\ldots+c_k\vec{x}^{(k)}=0$ is all c's being 0."

2024-06-10T14:27:05Z

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."

New page

[[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.

Linear independence (functions) - Revision history

Rice at 14:28, 10 June 2024

Rice: Created page with "Category:Differential Equations Given a set of functions \vec{x}^{(1)},\ldots,\vec{x}^{(k)} Defined in a < t < b. They are linearly independent of the only solution to c_1\vec{x}^{(1)}+\ldots+c_k\vec{x}^{(k)}=0 is all c's being 0."

Rice: Created page with "Category:Differential Equations Given a set of functions $\vec{x}^{(1)},\ldots,\vec{x}^{(k)}$ Defined in a < t < b. They are linearly independent of the only solution to $c_1\vec{x}^{(1)}+\ldots+c_k\vec{x}^{(k)}=0$ is all c's being 0."