What is a spanning set in Linear Algebra?
In: Mathematics
Spanning in laymen’s terms:
Spanning means it can go across / all-around.
Think of a vector as a line/segment.
If you add vectors together, you combine their direction.
A spanning set means you find combination between the vectors such that they can cover every direction in the space.
In order to do this, neither set can be a zero vector (unless the vector space has a zero there) and their combinations can’t all be going in the same direction (or else they can’t go whichever direction you want).
Meaning (0,0) & (2,3) can’t span R^2 and neither can (1,2) & (-2,-4), but (1,2) & (3,4) can.
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