Eigen Values and Vectors

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  Eigen v.

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 matrices
 Eigen v.
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)
 
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.
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