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In matrix algebra, if a matrix is positive...

In matrix algebra, if a matrix is positive definite, then all its eigenvalues are greater than zero.

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+2 votes

asked Jan 30, 2022 in Finite Element Method by Ava (110k points)

In matrix algebra, if a matrix is positive definite, then all its eigenvalues are greater than zero.

(a) True

(b) False

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

finite element method
flows of viscous incompressible fluids
velocity

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1 Answer

+1 vote

answered Jan 30, 2022 by James (185k points)
selected Feb 3, 2022 by Ava

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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