Basis vectors are a set of linearly independent vectors that span a vector space. They are used to express any vector in the space as a linear combination of the basis vectors.
The most common way to introduce basis vectors is by defining them as a set of vectors that form a basis for a vector space. It is important to explain the concept of linear independence and how the basis vectors can be used to represent any vector in the space.
Basis vectors are important because they provide a fundamental representation of a vector space. They allow for easy manipulation and calculation of vectors within the space, and they also aid in understanding the structure and properties of the space.
To identify basis vectors, you need to check if the set of vectors is linearly independent and spans the vector space. This can be done by setting up a matrix and performing row reduction to see if the vectors form a linearly independent set.
Yes, the basis vectors can change depending on the vector space. Different vector spaces may have different basis vectors, and even within the same vector space, the basis vectors may change depending on the choice of coordinate system.