# Orthogonal projection

See attached file for full problem description with symbols and equations.

---

Definition 11.1 An orthogonal projection operator is a linear transformation such that and .

Question:

If W is a subspace of V, prove that P_w is an orthogonal projection.

(P_w is P sub w)

© BrainMass Inc. brainmass.com October 9, 2019, 3:22 pm ad1c9bdddfhttps://brainmass.com/math/linear-transformation/orthogonal-projection-matrix-theory-2649

#### Solution Preview

Please see the attached file.

The orthogonal projection: satisfies: ,

Suppose is a subspace of , show that is also ...

#### Solution Summary

This is a proof regarding linear transformations and orthogonal projections are provided. The subspace with projections are examined.

$2.19