definition of orthogonal projection from vectors space with inner product into vectors subspace
Topics
About: vectors space
The table of contents of this article
Starting Context
- The reader knows a definition of %field name% vectors space.
- The reader knows a definition of inner product on real or complex vectors space.
- The reader knows a definition of projection from vectors space into vectors subspace.
Target Context
- The reader will have a definition of orthogonal projection from vectors space with inner product into vectors subspace.
Orientation
There is a list of definitions discussed so far in this site.
There is a list of propositions discussed so far in this site.
Main Body
1: Structured Description
Here is the rules of Structured Description.
Entities:
//
Conditions:
//
2: Note
This definition is not saying that for any
If there is such a
There are some typical cases in which
A typical case is that
Although it has used a basis, it does really depend on the choice of basis, because
Another typical case is that
When
Let us see that
For each