+2 votes
in Finite Element Method by (110k points)
In matrix algebra, if a matrix is positive definite, then all its eigenvalues are greater than zero.

(a) True

(b) False

I had been asked this question in a job interview.

Question is from Velocity in division Flows of Viscous Incompressible Fluids of Finite Element Method

1 Answer

+1 vote
by (185k points)
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Best answer
Right choice is (a) True

The explanation: A positive definite matrix is a symmetric matrix with all eigenvalues greater than zero. The FEM model of the continuity equation does not contain the pressure term, P. Therefore, the assembled equations also have zero in diagonal elements corresponding to the nodal values of P (i.e., the system of equations is not positive-definite).

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