7 Pages


K .l THE ALGORITHM A great many eigenvalue problems associated with vectors and tensors of problems in engineering and science are formulated in terms of three-dimensional Cartesian matrices composed of real elements. For such circumstances, the eigenvalue prob­ lem is amenable to a special treatment with a straightforward procedure in the computation. Let the matrix in question be represented as

In three dimensions, with real elements, adjoined to the other input data are the relationships incident to the geometry of the space itself; specifically, the orthonor­ mality of the coordinate frame of reference. The eigenvectors lie along principal axes that possess the ortho-normal property, and this adds an additional equation to the set of three equations for determining each eigenvalue. As a consequence, the sets of equations are rendered independent, so that the eigenvalues themselves can be computed.