7: Spectral Theory
- Page ID
- 14544
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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.