Information from 3Blue1Brown video series on Linear Algebra
The basis of a coordinate system is the 1 unit vectors needed to map out every point in that space - i.e 1 unit for x and y maps out 2D system.
Span is all the points a combination of vectors can reach if you had any scalar value.
Linear combination → Linear independence vs dependence - Linearly dependent means vectors that do not expand the span
Linear Transformations Linear transformations means gridlines must be evenly spaced and parallel to be linear
A linear transformation of a vector can be described by the basis vectors using ai + bj. Interestingly, if the basis gets transformed, you can use the new coordinates of i and j to calculate the linear transformation of a vector.