Independent in statistics and independent in linear algebra?

Question

In statistics it says two random variables are independent if and only if $F_{X,Y}=F_X(x)F_Y(y)$

If linear algebra it says:

Two or more functions (random variable is a function), equations, or vectors $f_1, f_2, ...,$ which are not linearly dependent, i.e., cannot be expressed in the form

$a_1f_1+a_2f_2+...+a_nf_n=0 $ with $a_1, a_2, ...$ constants which are not all zero are said to be linearly independent.

My question is :Are there any relationship between these two definitions?

Thanks.

Answer 1

If two vectors are linearly independent, they are orthogonal, and their dot product is zero. The covariance is equivalent to (n times) the dot product, and the correlation is the normalized dot product. Correlation and covariance are zero if the variates are independent.