If L=(a

_{1})(s

_{1}) + (a

_{2})(s

_{2}) + ... + (a

_{n})(s

_{n}) where a

_{1}, a

_{2}, ... ,a

_{n} are

scalar and s

_{1}, s

_{2}, ... s

_{n} are

vectors, then L is a

linear combination of s

_{1}, s

_{2}, ... , s

_{n}.

In English, that means that if you have some vectors, which are just n-tuples (pairs of numbers, or triplets, etc.), and you take a combination of them, for example one of the first, three of the second, and none of third, then that combination is called a linear combination of those three vectors. The reason it's called "linear" is because you are just taking a multiple of them, you're not multiplying them by anyting nasty, or squaring them, or anyting like that.

This term is used a lot in linear algebra.