Projection
Projection[u,v]
finds the projection of the vector u onto the vector v.
Projection[u,v,f]
finds projections with respect to the inner product function f.
Details

- For ordinary real vectors u and v, the projection is taken to be
.
- For ordinary complex vectors u and v, the projection is taken to be
, where
is Conjugate[v].
- In Projection[u,v,f], u and v can be any expressions or lists of expressions for which the inner product function f applied to pairs yields real results. »
- Projection[u,v,Dot] effectively assumes that all elements of u and v are real. »
Examples
open allclose allScope (9)
Find the projection of a machine-precision vector onto another:
Projection of a complex vector onto another:
Projection of an exact vector onto another:
Projection of an arbitrary-precision vector onto another:
The projection of large numerical vectors is computed efficiently:
Give an inner product of Dot to assume all expressions are real-valued:
Project vectors that are not lists using an explicit inner product:
Applications (2)
Find parallel and orthogonal components of a vector:
u is the sum of the parallel and orthogonal components:
Unnormalized Gram–Schmidt algorithm (use Orthogonalize for a better implementation):
Text
Wolfram Research (2007), Projection, Wolfram Language function, https://reference.wolfram.com/language/ref/Projection.html (updated 2014).
BibTeX
BibLaTeX
CMS
Wolfram Language. 2007. "Projection." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/Projection.html.
APA
Wolfram Language. (2007). Projection. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Projection.html