Probability that $n$ vectors drawn randomly from $\mathbb{R}^n$ are linearly independent Let's take $n$ vectors in $\mathbb{R}^n$ at random. What is the probability that these vectors are linearly independent? (i.e. they form a basis of $\mathbb{R}^n$)
(of course the problem is equivalent of "taken a matrix at random from $M_{\mathbb{R}}(n,n)$, what is the probability that its determinant $\neq 0$)
Don't know if this question is difficult to answer or not. Please share any information about it! :-)
(the $n$ vectors are meant with real values, I'm interested in solutions in $\mathbb{N}$ or $\mathbb{Q}$ or whatever fields you like)

This depend of how you takes the vectors. For the case $n=2$, for example, if you have a vector $v_1$, the probability that you get a vector LD with $v_1$ is $0$. So, the probability that you get two vector LI is 1.
