7: Spectral Theory — Read — Invisible Network

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7.1: Eigenvalues and Eigenvectors of a Matrix
Spectral Theory refers to the study of eigenvalues and eigenvectors of a matrix. It is of fundamental importance in many areas and is the subject of our study for this chapter.
7.2: Diagonalization
When a matrix is similar to a diagonal matrix, the matrix is said to be diagonalizable.
7.3: Applications of Spectral Theory
Suppose we have a matrix A and we want to find A50 . One could try to multiply A with itself 50 times, but this is computationally extremely intensive (try it!). However diagonalization allows us to compute high powers of a matrix relatively easily.
7.4: Orthogonality
7.E: Exercises

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