help me understand a line in an "ATA is positive, semi-definite" proof I am looking at a proof for why ATA is positive semi-definite when A is nxn and it has this line. vTAATv = ATv • ATv ≥ 0. I understand what vTAATv means and the purpose of proving that it's nonnegative, etc... My problem is that I am a linear algebra novice and do not necessarily understand how the first part vTAATv is equivalent to ATv • ATv. I know that aTb = a • b, but something else is going on, no? Appreciate any help!