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What is Eigenvalues

Handbook of Research on Systems Biology Applications in Medicine
In linear algebra the equation defines the eigenvalues ? and the corresponding eigenvectors v of a linear transformation represented by a quadratic matrix A. ? is a complex value and v is a complex valued vector. The eigenvalues describe essential characteristics of the linear map.
Published in Chapter:
Deterministic Modeling in Medicine
Elisabeth Maschke-Dutz (Max Planck Institute for Molecular Genetics, Germany)
Copyright: © 2009 |Pages: 23
DOI: 10.4018/978-1-60566-076-9.ch004
Abstract
In this chapter basic mathematical methods for the deterministic kinetic modeling of biochemical systems are described. Mathematical analysis methods, the respective algorithms, and appropriate tools and resources, as well as established standards for data exchange, model representations and definitions are presented. The methods comprise time-course simulations, steady state search, parameter scanning, and metabolic control analysis among others. An application is demonstrated using a test case model that describes parts of the extrinsic apoptosis pathway and a small example network demonstrates an implementation of metabolic control analysis.
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Multi-Degrees of Freedom System and Hydrodynamic Principle
Mathematically each of a set of values of a parameter for which a differential equation has a non-zero solution (an eigenfunction) under given conditions.
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