The mass matrix is the Gram matrix of a finite element basis in the L2 inner product. Its coefficient quadratic form is the squared L2 norm of the represented trial function, so it is a positive-definite matrix for a linearly independent basis.
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The mass matrix is a mathematical construct used in various fields, particularly in mechanics and numerical analysis. It is often associated with systems of particles or rigid bodies, and it plays a crucial role in the formulation of dynamic equations of motion. ### Definition: In the context of finite element analysis (FEA) and structural dynamics, the mass matrix represents the distribution of mass in a system and connects the nodal accelerations to the resulting forces.