An Electrical Network for Determining the Eigenvalues and Eigenvectors of a Real Symmetric Matrix
作者:
Abraham Many,
Saul Meiboom,
期刊:
Review of Scientific Instruments
(AIP Available online 1947)
卷期:
Volume 18,
issue 11
页码: 831-836
ISSN:0034-6748
年代: 1947
DOI:10.1063/1.1740856
出版商: AIP
数据来源: AIP
摘要:
An electrical network for determining the eigenvalues and eigenvectors of a real symmetric matrix of ordernis described. It consists ofn 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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