Thoughts of a Flying Sheep

Ready for some linear algebraic trivia? Let B be a bilinear form on R^n. An nxn matrix g is called an automorphism of B is
B(gX, gY) = B(X, Y) for all X, Y in R^n. Show that, for any bilinear form on R^n, the collection of automorphisms (with
the regular matrix multiplication) forms a group. This is called the orthogonal group of the form B.


Hint: Let G be the above collection. One way of proving this is to show the following three things: the identity matrix is in G, if g is in G, then g^-1 is in G, and if g,h are in G, then so is the product gh.

It should be fairly straightfoward. Good luck!

posted by FlyingSheep @ 2:59 PM