Abstract
In this chapter we introduce elements of graph theory, graphs of components, matrix formulation of Kirchhoff’s laws, matrix associated spaces, and Tellegen’s theorem.
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Notes
- 1.
Leonhard Euler (1707–1783) was a Swiss mathematician, physicist, astronomer, logician, and engineer who made important and influential discoveries in many branches of mathematics.
- 2.
The set is complete if any further KVL or KCL equation is linearly dependent on the equations belonging to the set.
References
Euler L (1741) Solutio Problematis ad Geometriam Situs Pertinentis. Commentarii Academiae Scientiarum Imperialis Petropolitanae 8:128–140
Kuratowski C (1930) Sur le problème des courbes gauches en topologie. Fund. Math. 15:271–283
Meyer CD (2000) Matrix analysis and applied linear algebra. SIAM, Philadelphia
Laub AJ (2005) Matrix analysis for scientists and engineers. SIAM, Philadelphia
Penfield P, Spence R, Duinker S (1970) Tellegen’s theorem and electrical networks. MIT Press, Cambridge
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Parodi, M., Storace, M. (2018). Advanced Concepts. In: Linear and Nonlinear Circuits: Basic & Advanced Concepts. Lecture Notes in Electrical Engineering, vol 441. Springer, Cham. https://doi.org/10.1007/978-3-319-61234-8_2
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DOI: https://doi.org/10.1007/978-3-319-61234-8_2
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