# totaly positive matrix method

• Sep 24th 2011, 10:16 AM
transgalactic
totaly positive matrix method
cant understand the way the book tests if a matrix is totaly positive(dont know the proper term)
we need to show that $\displaystyle \sum_{i=1}^{2}\sum_{j=1}^{2}a_{ij}k_{i}\overline{k _{j}}>0$
ihave this matrix but
$\displaystyle \left(\begin{array}{cc}0 & i\\-i & 0\end{array}\right)$
so they choose $\displaystyle k_{1}=1$$\displaystyle k_{2}=0$ and got that the expession is =0
but we have 4 members here
so we need k for each member thus we need 4 k's
why 2?
cant understand how this method works
?
• Sep 24th 2011, 11:15 AM
HallsofIvy
Re: totaly positive matrix method
The phrase you want is "positive definite". However, the definition of "positive definite" varys depending on the type of matrix (real entries, complex entries, complex entries and the matrix is Hermitian). What kind of matrices are you dealing with and what is your definition of "positive definite"? (What you want to prove looks awfully like one of the definitions.)
• Sep 24th 2011, 11:58 AM
transgalactic
Re: totaly positive matrix method
yes if its hermitic and this double sum its bigger and zero
then its positive definite.

its matrices in complex field

but i dont understand how this double sum condition works

i am stuck on this 2x2 matrices given above

?