Hi Krishna, This is a classic linear algebra result - a symmetric matrix is positive definite if and only if it has positive pivots. Since this matrix has a zero block it does not even have a full set of pivots so it cannot be positive definite.
Thanks, David Wells On Sat, Feb 1, 2020 at 9:49 AM Krishnakumar Gopalakrishnan <[email protected]> wrote: > > I realize that this question is not exactly about the code/concepts behind > deal.II library itself, but rather about a mathematical statement from > step-20. > > "After assembling the linear system we are faced with the task of solving it. > The problem here is: the matrix has a zero block at the bottom right (there > is no term in the bilinear form that couples the pressure p with the pressure > test function q), and it is indefinite". > > My question is about the indefiniteness of the matrix. In my understanding, a > matrix is indefinite if it has both positive and negative eigen values. > However, there has not been any discussion thus far in step-20 that comment > about the eigen-values. How was the statement about the indefiniteness then > made? Can someone here explain why that matrix is indefinite? > > Regards, > Krishna > > -- > The deal.II project is located at http://www.dealii.org/ > For mailing list/forum options, see > https://groups.google.com/d/forum/dealii?hl=en > --- > You received this message because you are subscribed to the Google Groups > "deal.II User Group" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/dealii/ec88d69a-4b26-43cb-915b-b3ae1fdfa3aa%40googlegroups.com. -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/CABrTbYSFeSScPWYbGdrZU9mwGekXgznDodHu%3Dr-yKs12on%3DF5A%40mail.gmail.com.
