In linear algebra, a Hessenberg matrix is a special kind of square matrix, one that is `almost` triangular. To be exact, an upper Hessenberg matrix has zero entries below the first subdiagonal, and a lower Hessenberg matrix has zero entries above the first superdiagonal. They are named after Karl Hessenberg. is lower Hessenberg. ==Computer progr.....
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http://en.wikipedia.org/wiki/Hessenberg_matrix
An upper Hessenberg matrix is a square matrix with A(i, j)=0 for i > j+1. A lower Hessenberg matrix is one whose transpose is upper Hessenberg.
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http://glossary.computing.society.informs.org/index.php?page=H.html
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