Eigenvalues and Eigenvectors

If the solution of a linear system is compared to the gift of fish, an analysis of the linear transformation represented by a matrix, in terms of its eigenvalues and eigenvectors, becomes comparable to instructions in the art of fishing. With a knowledge of eigenvalues and eigenvectors of a matrix, the complete behaviour of the transformation can be understood and explained with full insight and confidence. In this chapter, we carry out a foundational groundwork of the eigenvalue problem, the methods of which will be covered in detail in the following chapters.

Eigenvalue Problem

Let us get back to our old theme of Chap. 2: a matrix represents a linear transformation, operates on vectors in its domain and maps them ...

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