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I am not sure if this question has been asked before, apologies if I am repeating this question again.

My question is as follows:

given a set i know how to find all the subsets of the set.

But what I would really like to know is how do i find all linearly independent subsets that can be obtained from this super set.

Thanks, Bhavya

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    @Andre thank you for the explanation it makes a lot of sense2012-01-24

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Here is a simple method (not efficient necessarily). If the subset is finite (or has a finite generator), let call it $S=\lbrace a_i\rbrace_{i=1}^n$, on a v.e. $E$ with coefficients in $\mathbb{K}$, try to solve the equation $\sum_{i=1}^n\lambda_ia_i=0$ where $\lambda_i\in\mathbb{K}$. Then if exist $\lambda_i\neq0$, eliminate $a_i$ from $S$. Repeat until the solution is $\lambda_i=0, \forall i$. Then, all the subsets of $S$ (actualized) will be l.i. After try to interchange elements from $S$ with the eliminated preserving the linear independence.