Matrix eigenvalue analysis

We shall encounter numerous situations in which eigenvalue analysis provides insight into the behavior and performance of an algorithm, or is itself of direct use, as when estimating the vibrational frequencies of a structure or when calculating the states of a system in quantum mechanics. The related method of singular value decomposition (SVD), an extension of eigenvalue analysis to nonsquare matrices, is also discussed. 

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Our discussion is intended only to provide a foundation in linear algebra for the practice of numerical computing, and is continued in Chapter 3 with a discussion of matrix eigenvalue analysis. For a broader, more detailed, study of linear algebra, consult Strang (2003) or Golnb van Loan (1996). 

This text first presents a fundamental discussion of linear algebra, to provide the necessary foundation to read the applied mathematical literature and progress further on one s own. Next, a broad array of simulation techniques is presented to solve problems involving systems of nonlinear algebraic equations, initial value problems of ordinary differential and differential-algebraic (DAE) systems, optimizations, and boundary value problems of ordinary and partial differential equations. A treatment of matrix eigenvalue analysis is included, as it is fundamental to analyzing these simulation techniques. 

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