00:01
Hello, so here we are told that if we have n by n matrices, a and b, that are orthogonal, we want to know must a plus b also be orthogonal.
00:12
So if we suppose that a and b, again, are n by n orthogonal matrices, then we have to have that a times a transpose equals to the identity, and b times b transpose is also equal to the identity.
00:28
So here we can look at a plus b transpose times a plus b.
00:41
Well, that is going to be equal to a transpose plus b transpose plus a transpose times a plus b, which is then going to be equal to a transpose plus a transpose plus a transpose plus b, which then is going to be equal to a transpose a transpose a plus b transpose b, which then is going to be equal to a transpose a plus b transpose a plus b transpose a plus b.
01:08
A, plus a transpose b, plus b transpose b, which is then going to be equal to two times the identity plus b...