On the inversion of the Cauer-Routh matrix

Ingram, W. H.

doi:10.1090/qam/99829

Author: W. H. Ingram
Journal: Quart. Appl. Math. 27 (1969), 215-222
DOI: https://doi.org/10.1090/qam/99829
MathSciNet review: QAM99829
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References | Additional Information

Edward John Routh, The advanced part of a treatise on the dynamics of a system of rigid bodies. Being part II of a treatise on the whole subject, Dover Publications, Inc., New York, 1955. 6th ed. MR 0068369
Wilhelm Cauer, Untersuchungen über ein Problem, das drei positiv definite quadratische Formen mit Streckenkomplexen in Beziehung setzt, Math. Ann. 105 (1931), no. 1, 86–132 (German). MR 1512706, DOI https://doi.org/10.1007/BF01455810
W. H. Ingram and C. M. Cramlet, On the foundations of electrical network theory, J. Math. Phys. Mass. Inst. Tech. 23 (1944), 134–155. MR 15330, DOI https://doi.org/10.1002/sapm1944231134

H. F. Bückner, Die Anwendung elektronischer Rechenmaschinen in der Starkstromtechnik, Buchreihe Band 3, VDE-Verlag, Berlin, 1958.

R. Braae, Matrix analysis for electrical engineers, Pitman, 1963. A proof of Bückner’s formula for the case $L = {K_T}$ is given on p. 47 and for the general case on p. 143; both proofs are simpler than Bückner’s unpublisher proof.