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