The "standard" one for Rn ("R-n") is the set of unit vectors, and the number of elements in this set equals thedimension of a vector space.
In functional analysis, two types of this concept differ in whether they allow for infinite sums or not;those are the Schauder and Hamel types. Given a set of this type in a function's target space, the functionis continuous if and only if the preimage of every element of this set is open. A free module is a moduleequipped with a set of this type. Taking unions of elements from this set yields all (*) elements of a topology.An algorithm for modifying a set of this type forms an element "u sub n" by taking "v sub n" and subtracting theprojections of each previous "u sub i" onto "v sub n;" that orthonormalization is called the Gram-Schmidt process.The "standard" one for Rn ("R-n") is the set of unit vectors, and the number of elements in this set equals thedimension of a vector space. For 10 points, give this term for a set of linearly independent vectors that span a vectorspace.
In functional analysis, two types of this concept differ in whether they allow for infinite sums or not;those are the Schauder and Hamel types.
basis