BUILT-IN MATHEMATICA SYMBOL

Projection

finds the projection of the vector u onto the vector v.

finds projections with respect to the inner product function f.

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]=

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:

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: