The stiffness matrix is the n-element square matrix A defined by
By defining the vector F with components Fi = (φi, f), the coefficients ui are determined by the linear system AU = F. The stiffness matrix is symmetric, i.e. Aij = Aji, so all its eigenvalues are real. Moreover, it is a strictly positive-definite matrix, so that the system AU = F always has a unique solution. (For other problems, these nice properties will be lost.)
Note that the stiffness matrix will be different depending on the computational grid used for the domain and what type of finite element is used. For example, the stiffness matrix when piecewise quadratic finite elements are used will have more degrees of freedom than piecewise linear elements.
Read more about Stiffness Matrix: The Stiffness Matrix For Other Problems, Practical Assembly of The Stiffness Matrix
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