Vectors

Question 1

What’s the preferred way to think about the entries in a vector.

Answer 1

A vector is collection of coordinates that scale the basis vectors.

Question 2

What does it by a set of vectors being linearly dependent?

Answer 2

In the theory of vector spaces, a set of vectors is said to be linearly dependent if at least one of the vectors in the set can be defined as a linear combination of the others; if no vector in the set can be written in this way, then the vectors are said to be linearly independent. These concepts are central to the definition of dimension.[1]

A vector space can be of finite-dimension or infinite-dimension depending on the number of linearly independent basis vectors. The definition of linear dependence and the ability to determine whether a subset of vectors in a vector space is linearly dependent are central to determining a basis for a vector space.