I am looking at a proof for why A^{T}A is positive semi-definite when A is nxn and it has this line.I understand what

v^{T}AA^{T}v = A^{T}v • A^{T}v ≥ 0.

vmeans 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^{T}AA^{T}vvis equivalent to^{T}AA^{T}vAI know that a^{T}v • A^{T}v.^{T}b = a•b, but something else is going on, no? Appreciate any help!