Linearly Independent

==2024-12-11

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Independence is stable

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Theory

Given a Set of vectors $A$ defined over a Field $\mathbb{F}$, $A$ is said to be Linearly Independent if $\exists$ scalars ${\alpha }_1,{\alpha }_2,{\alpha }_3,\dots ,{\alpha }_{n_o(A)}\in \mathbb{F}$ such that the equation: ${\alpha }_1{a}_1+{\alpha }_2{a}_2+{\alpha }_3{a}_3+\cdots +{\alpha }_{n_o(A)}{a}_{n_o(A)}=0$ has only trivial solution.

That means all the scalars are zero.

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PTR