Orthogonal projectiongeometry, an orthogonal projection of a k-dimensional object onto a d-dimensional hyperplane (d < k) is obtained by intersections of (k − d)- dimensional hyperplanes drawn through the points of an object orthogonally to the d-hyperplane. In particular, an orthogonal projection of a three-dimensional object onto a plane is obtained by intersections of planes drawn through all points of the object orthogonally to the plane of projection.
If such a projection leaves the origin fixed, it is a self-adjoint idempotent linear transformation; its matrix is a symmetric idempotent matrix. Conversely, every symmetric idempotent matrix is the matrix of the orthogonal projection onto its own column space. If M and n×k is a matrix with more rows than columns, the k columns spanning a k-dimensional subspace of an n-dimensional space, then the matrix of the orthogonal projection onto the column space of M is
A related concept is used in technical drawing, where orthogonal projection, more correctly called orthographic projection, is drawing of the views of an object projected onto orthogonal planes. Commonly known views of this type are plan (plan view), side view and elevation.