`Gear' is simple defective,
It can be rank deficient and
can have double and triple eigenvalues.
It is tri-diagonal with zero diagonal and ones on the sub- and
super-diagonals, but with the addition of
A1,J = ±1
AN,N-K+1 = ±1.
The eigenvalues and eigenvectors are of known explicit form and can
be computed here.
The matrix can have double and triple eigenvalues and can be defective.
- This generator is adapted from Nicholas J. Higham's
Test Matrix Toolbox.
- C.W. Gear, A simple set of test matrices for eigenvalue programs,
Math. Comp., 23 (1969), pp. 119-125.
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Page created 1997-03-03, last modified 2000-08-06.