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A 8*8 matrix
with the eigenvalues +/- 10sqrt(10405)
(1020.049...) 1000 (double) and
two more eigenvalues 1019... and 1020,
that means a cluster of 5 nearby values, two different but
absolutely dominant values and in addition the eigenvalues
0 and 510-100sqrt(26)=0.09805.
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the "bar matrix" (quindiagonal)
with diagonals 1,..,1; -4,...,-4;
5,6,..,6,5; -4,...,-4; 1,...1,
and the eigenvalues 16*sin(i*pi/(2(n+1)))**4, i = 1,...,n.
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Formation of a matrix by back calculation from a fixed given
unitary eigensystem Rij = (sin(ij*pi/(n+1))*sqrt(2/(n+1)), i,j = 1....,n
and eigenvalues which are entered here. The entries must be separated by
commas or blanks. If an eigenvalue Ei arises m-times, then you can use
the following short hand notation: m*Ei (3*7, instead of 7,7,7, )
The input can extend over several lines.
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complete input of a symmetric matrix by its lower triangle.
input is rowwise, each row begins on a new input line but may extend over several lines.
values separated by comma or blank space. a successive occurence of m values E
can be abbreviated as m*E (3*0, instead of 0,0,0, )
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