Question

Suppose A is an orthogonal matrix. Show that |λ| = 1 for all eigen-

values λ. (Hint: start off with an eigenvector and dot-product it with itself.

Then cleverly insert A and At into the dot-product.)

b) Suppose P is an orthogonal projection. Show that the only possible

eigenvalues are 0 and 1. (Hint: start off with an eigenvector and write down

the definition. Then apply P to both sides.)

An n×n matrix B is symmetric if B = Bt. Note that this is half of being

an orthogonal projection. These are particularly easy matrices to eyeball!

Answer 1