- #1
yooyo
- 7
- 0
Could a set of n verctors in Rm span all of Rm when n<m?
any hits? kinda confused with this span thing.
any hits? kinda confused with this span thing.
The span of a set of vectors is the set of all possible linear combinations of those vectors. In other words, it is the set of all vectors that can be created by multiplying each vector by a scalar and adding them together.
The dimensionality of a vector space is the number of vectors needed to span the space. In other words, it is the minimum number of vectors required to create every possible vector in the space through linear combinations.
No, a set of n vectors in Rm cannot span all of Rm when n>m. This is because there are more dimensions in Rm than there are vectors, so there will always be some vectors that cannot be created through linear combinations of the given vectors.
Yes, a set of n vectors in Rm can span all of Rm when n=m. This is because there are exactly enough vectors to create every possible vector in the space through linear combinations.
Yes, a set of n vectors in Rm can span all of Rm when n
Similar threads
Linear and Abstract Algebra
Linear and Abstract Algebra
Calculus and Beyond Homework Help
Linear and Abstract Algebra
Linear and Abstract Algebra
Challenge
Math Challenge - August 2021
Linear and Abstract Algebra
Linear and Abstract Algebra
Linear and Abstract Algebra
Share: