[University] How do you define a plane as a subspace of R^n?
How do you define a plane in R^n where n>3? I know how to do it in R^(3), but I'm not sure if you can just extend that to R^(n).
Posted Dec 4, 2014, 9:23 PM UTC
24
One way is picking two linearly-independent vectors. They form a basis for the subspace, which you know is dimension 2 because they're independent.
2
There are different ways in R^(3), which do you want to generalize? Also, by a plane in R^(n) do you mean a 2 dimensional subspace or an n-1 dimensional subspace?
n-1 dim subspace is called a hyperplane
Who's to say whether or not OP has heard the term "hyperplane"?