what exactly is a basis?
all these textbook explantions are so confusing to me and usually have all kinds of symbols that I have to decipher making it even harder to read let alone understand.
For example, is a basis for over . Because anything in can be expressed in terms of those.
*)By "expressed" I mean as a linear combination of those vectors.
If any vectors in a set are linear combinations of each other then they are linearly dependent and not a basis.but I thought if they were linear combinations that means they are linearly dependent and therefore are not a basis of that subplace or whatever they call it...lol
If a set is a basis of a space then every vector in the space is a linear combination of the vectors in the basis.