Hello all. I have a fairly rudimentary knowledge of matrices and broader linear algebra. This gets me in a lot of trouble when I'm following along the math of something fine and then I run into some matrix stuff and get stumped, like this. I'm a little bit confused on taking the inner product from the Minkowski Tensor to the actual number. I understand why (in the context of spacetime intervals) it makes sense to define the metric as diag(-1,1,1,1) = [itex]\eta[/itex][itex]\alpha\beta[/itex] What I don't get is that if you define the inner product of two vectors [itex]A[/itex] and [itex]B[/itex] as [itex]\eta[/itex][itex]\alpha\beta[/itex]A[itex]\alpha[/itex]B[itex]\beta[/itex] (I hope I got the summation convention right), how do you get from the matrix form to the number -t[itex]\alpha[/itex]t[itex]\beta[/itex]+x[itex]\alpha[/itex]x[itex]\beta[/itex] ....(and so on)? It is just a rule of matrices I don't know? Or is it a specific thing in this context. Thank you Also, unrelated: my textbook didn't explicitly say that the spacetime interval (squared) is equal to the inner product, is that true?