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

Project onto another vector:

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:

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: