psholder
- 1
- 0
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!
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!
)