Howtosignalprocessing
- What is orthogonal projection?
- How do you find orthogonal projections?
- What is the purpose of orthogonal projection?
- What is orthogonal projection of a line?
What is orthogonal projection?
A projection of a figure by parallel rays. In such a projection, tangencies are preserved. Parallel lines project to parallel lines.
How do you find orthogonal projections?
Example(Orthogonal projection onto a line)
By the theorem, to find x L we must solve the matrix equation u T uc = u T x , where we regard u as an n × 1 matrix (the column space of this matrix is exactly L ! ). But u T u = u · u and u T x = u · x , so c =(
What is the purpose of orthogonal projection?
The orthogonal projection minimizes the distance
The distance between two vectors is measured by the norm of their difference. we have used Pythagoras' theorem.
What is orthogonal projection of a line?
The orthogonal projection of a line onto a plane is a line or a point. If a line is perpendicular to a plane, its projection is a point. The intersection point with the plane and its direction vector s will be coincident with the normal vector N of the plane.
