An Electrical Network for Determining the Eigenvalues and Eigenvectors of a Real Symmetric Matrix

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Abstract
An electrical network for determining the eigenvalues and eigenvectors of a real symmetric matrix of order n is described. It consists of n LC‐circuits, each one coupled to each of the others by two condensers. The values of the condensers are adjusted according to the elements of the matrix. Both positive and negative values of the elements can be dealt with by changing the connections of the coupling condensers. The network is excited by a variable frequency source, the resonance frequencies being observed on an oscillograph. The eigenvalues are given by these resonance frequencies and the components of the eigenvectors by the voltages across the coils. The construction of the network and the operating procedure are described. The theory of the network when losses in the coils are taken into account is also given, and the case of multiple roots is discussed. The accuracy of the eigenvalues obtained is better than 0.1 percent of the greatest eigenvalue, while the accuracy of each eigenvector is about one percent of its greatest component.

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