Project the vector (5, 6, 7) onto the axis:

Project onto another vector:

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:

Project symbolic vectors:

Give an inner product of Dot to assume all expressions are real-valued:

Project vectors that are not lists using an explicit inner product:

Specify the inner product using a pure function:

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):

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: