- #1
strobeda
- 42
- 0
I may have a bad day, or not enough coffee yet.
So,
"If A is a nonempty subset of a vector space V, then the set
L(A) of all linear combinations of the vectors in A is a subspace, and it is
the smallest subspace of V which includes the set A.
If A is infinite, we obviously can't use a single finite listing. However, the
sum of two linear combinations of elements of A is
clearly a finite sum of scalars times elements of A."
Question:
If A is infinite, how can the sum of its linear combinations be finite (even choosing a finite sum of scalars)?
Thank you.
So,
"If A is a nonempty subset of a vector space V, then the set
L(A) of all linear combinations of the vectors in A is a subspace, and it is
the smallest subspace of V which includes the set A.
If A is infinite, we obviously can't use a single finite listing. However, the
sum of two linear combinations of elements of A is
clearly a finite sum of scalars times elements of A."
Question:
If A is infinite, how can the sum of its linear combinations be finite (even choosing a finite sum of scalars)?
Thank you.