Today the TA for my quantum mechanics class told me that the inner product $\langle-x|-x\rangle=-1$. This makes no sense to me and I've never heard of this before (that I can remember). How could this possibly be true when the inner product is $\langle f,g\rangle := \int_a^bf(t)g(t)dt$? She told me "when you dot a negative vector with another negative vector it stays in the $-x$ plane." That I could potentially see making sense, but I don't see how this could possibly be true when you look at the integral form of the inner product.
Is this correct?