`Gear' is simple defective, singular matrix. 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 and 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.


  1. This generator is adapted from Nicholas J. Higham's Test Matrix Toolbox.
  2. 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. [ ]