This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# Projection

 Projection finds the projection of the vector u onto the vector v. Projectionfinds projections with respect to the inner product function f.
• For ordinary vectors u and v, the projection is taken to be . »
• In Projection, u and v can be any expressions or lists of expressions for which the inner product function f applied to pairs yields real results. »
Project the vector (5, 6, 7) onto the x axis:
Project onto another vector:
Project the vector (5, 6, 7) onto the x axis:
 Out[1]=

Project onto another vector:
 Out[1]=
 Scope   (4)
Use symbolic vectors:
Assume all variables are real:
Use exact arithmetic to find the projection of u onto v:
Use machine arithmetic:
Use 20-digit precision arithmetic:
Projection of a complex vector onto another:
Use a different inner product:
 Applications   (2)
Find parallel and orthogonal components of a vector:
is the sum of the parallel and orthogonal components:
Unnormalized Gram-Schmidt algorithm (use Orthogonalize for a better implementation):
Do Gram-Schmidt on a random set of 3 vectors:
Verify orthogonality:
Generate some orthogonal polynomials:
The projection of u onto v is in the direction of v:
For ordinary vectors u and v, the projection is taken to be :
The projection of u onto v is equivalent to multiplication by an outer product matrix:
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