# Orthogonal Projection onto a Subspace

03/08/2011

**Revisit**:

- Let P be an orthogonal projection matrix, then and .
- x and y are two vectors. The projection of y onto x is .

**New** **question**: Let . y is an vector. What is the projection of y onto the column space of A?

**Answer**:

**Proof**: it is the same to find x to minimize which is a least squares problem. As we know, the answer is . Then the projection is . Hence the projector is .

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