Linear Combination - The Linear Span

The Linear Span

Main article: linear span

Take an arbitrary field K, an arbitrary vector space V, and let v1,...,vn be vectors (in V). It’s interesting to consider the set of all linear combinations of these vectors. This set is called the linear span (or just span) of the vectors, say S ={v1,...,vn}. We write the span of S as span(S) or sp(S):

Read more about this topic:  Linear Combination

Famous quotes containing the word span:

    “A tree that can fill the span of a man’s arms
    Grows from a downy tip;
    A terrace nine stories high
    Rises from hodfuls of earth;
    A journey of a thousand miles
    Starts from beneath one’s feet.”
    —Lao-Tzu (6th century B.C.)