Much of linear algebra and multivariate calculus is in in
This is the space of ordered lists of real numbers
We are used to working in and , but higher dimensions are no more complicated
The lists of numbers just get larger
We write the elements of as columns instead of rows, to be consistent with notation of
We can interpret lists of numbers as either points or vectors
If the list represents some absolute state or position, it is a point
The position of some object, the current stock prices, the current temperature
If it represents a relative change of state, it is a vector
For example, a displacement in positions, change in stock prices, change in temperature
The difference between points and vectors are not just that vectors have direction and magnitude, as some vectors can be 1 dimensional and represent a change in state, and points can have many dimensions and represent a state.