finds the projection of the vector u onto the vector v.
finds projections with respect to the inner product function f.
- 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. »
Examplesopen allclose all
Give an inner product of Dot to assume all expressions are real-valued:
Unnormalized Gram–Schmidt algorithm (use Orthogonalize for a better implementation):
Wolfram Research (2007), Projection, Wolfram Language function, https://reference.wolfram.com/language/ref/Projection.html (updated 2014).
Wolfram Language. 2007. "Projection." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/Projection.html.
Wolfram Language. (2007). Projection. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Projection.html