D
D
d0lph1n2018-12-21 20:45:05
Mathematics
d0lph1n, 2018-12-21 20:45:05

How is a plane mathematically described in a finite-dimensional Euclidean space?

Question for mathematicians (geometers, probably) about how to set an M-dimensional plane (M <= N) in an N-dimensional Euclidean space.
I understand this at the level of 3-dimensional space: that
(1) there is a "basic" plane, given through 3 "basic" variables (x, y, z),
(2) there is a line at the intersection of 2 planes, given as a system equations of 2 planes,
(3) is a point lying at the intersection of 3 planes, given as a system of equations of 3 planes or as a vector (x, y, z).
Is it true that the plane of dimension Nk is given by a system of k+1 equations (0 <= k < N-1)? Is this true for Euclidean spaces of higher dimension?
Where can I read about this, briefly and with a presentation on the example (or by analogy) of 3-dimensional space?
ps Is a point considered a plane of zero dimension?

Answer the question

In order to leave comments, you need to log in

1 answer(s)
A
AVKor, 2018-12-21
@AVKor

Here .

Didn't find what you were looking for?

Ask your question

Ask a Question

731 491 924 answers to any question