• ← Normalize
• → UnitVector

Projection

WMA link

Projection[u, v]

gives the projection of the vector u onto v

For vectors u and v, the projection is taken to be ( v . u / v . v ) v

For complex vectors u and v, the projection is taken to be ( v* . u / v* . v ) v where v* is Conjugate[v].

Projection of two three-dimensional Integer vectors:

• • Projection[{5, 6, 7}, {1, 0, 0}]

Projection of two two-dimensional Integer vectors:

• • Projection[{2, 3}, {1, 2}]

Projection of a machine-precision vector onto another:

• • Projection[{1.3, 2.1, 3.1}, {-0.3, 4.2, 5.3}]

Projection of two complex vectors:

• • Projection[{3 + I, 2, 2 - I}, {2, 4, 5 I}]

Project a symbol vector onto a numeric vector:

• • Projection[{a, b, c}, {1, 1, 1}]

The projection of vector u onto vector v is in the direction of v:

• • {u, v} = RandomReal[1, {2, 6}];

• • Abs[VectorAngle[Projection[u, v], v]] < 0. + 10^-7