Eigen Values and Vectors
- A symmetric real-valued matrix times an arbitrary vector:
- for example.
- A symmetric N×N matrix has N real Eigen-values (not necessarily distinct).
- The naive Eigen-value algorithm finds
- The naive algorithm is easy to understand, but is slow, finds only the |largest| Eigen-value (without extra work), and is not always accurate.
- The Jacobi Eigen-value algorithm finds
-
- (random example computed by JavaScript)
- (random example computed by JavaScript)
- performs much better and returns all the Eigen-values and Eigen-vectors.
- There are many other Eigen-value algorithms.
- An Eigen-value finding algorithm is used in Kearsley's method for the 3-D superposition problem.