# Linear algebra

by math6
Tags: algebra, linear
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,693 I have moved this to the "Linear and Abstract Algebra" forum. What, exactly, do you want to do. You say you are given a basis for a vector space and "want to define a family of vectors". Is this family supposed to have any special property? There are an infinite number of ways to write a family of vectors in terms of a basis. A "one parameter" family would be of the for $\{f_1(t) e_1+ f_2(t)e_2+ \cdot\cdot\cdot+ f_n(t)e_n\}$ where n is the dimension of the space and $f_i(t)$ are n specific functions of the parameter t. We could similarly define "two parameter", etc. families of vectors. Your question is just too general to have a simple answer.