Symmetric matrices and orthogonal projections

[Tonyt88]

Homework Statement

Consider a symmetric n x n matrix A with A² = A. Is the linear transformation T(x) = Ax necessarily the orthogonal projection onto a subspace IR^n?

Homework Equations

The Attempt at a Solution

No idea what thought to begin with.

 

[Dick]

If A is symmetric over the reals then it can be diagonalized. What does that tell you? What is a projection?