is a positive definite matrix necessarily symmetric?
Also if A is an nxn matrix and is singular (not invertible) then there is an x in Rn such that Ax=0 right?
No! for example the matrix is positive definite but not symmetric. to see why is positive
definite, let . then see that
right! in fact for some if and only if is not invertible.Also if A is an nxn matrix and is singular (not invertible) then there is an x in Rn such that Ax=0 right?
No! being Hermitian is not a part of the definition. an matrix over is positive definite if
if all entries of are real, then it's easy to see that in order to prove that is positive definite, we only need to show that
using this fact, we can see easier why the matrix in my previous post is positive definite.
if is Hermitian, then is positive definite if because for a Hermitian matrix