![]() ![]() It should be emphasized that finding eigenvalues involves asking for the determinant of an n × n matrix with entries polynomials, which is slow. We do not discuss computational aspects of eigenvalues/eigenvectorsĭetermination-there are lots of algorithms, and computer codes for doing it, symbolically (precisely) and approximately, for general matrices and special classes of matrices. The determination of the eigenvalues and eigenvectors of a system is extremely important in physics and engineering, where it arises in such common applications as stability analysis, the physics of rotating bodies, and small oscillations of vibrating systems, to name only a few. Introduction to Linear Algebra with Mathematica GlossaryĮigenvalues (translated from German, meaning "proper values") are a special set of scalars associated with every square matrix that are sometimes also known as characteristic roots, characteristic values, or proper values.Įach eigenvalue is paired with a corresponding set of so-called eigenvectors. ![]() Return to the main page for the second course APMA0340 Return to the main page for the first course APMA0330 Return to Mathematica tutorial for the second course APMA0340 Return to Mathematica tutorial for the first course APMA0330 Return to computing page for the second course APMA0340 Return to computing page for the first course APMA0330 Laplace equation in spherical coordinates. ![]()
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