Hessenberg Matrix
A Hessenberg matrix is a matrix of the form
![画像: [a_(11) a_(12) a_(13) ... a_(1(n-1)) a_(1n); a_(21) a_(22) a_(23) ... a_(2(n-1)) a_(2n); 0 a_(32) a_(33) ... a_(3(n-1)) a_(3n); 0 0 a_(43) ... a_(4(n-1)) a_(4n); 0 0 0 ... a_(5(n-1)) a_(5n); | | | | | |; 0 0 0 a_((n-1)(n-2)) a_((n-1)(n-1)) a_((n-1)n); 0 0 0 0 a_(n(n-1)) a_(nn)].](/index.cgi/larger-text/https://mathworld.wolfram.com/images/equations/HessenbergMatrix/NumberedEquation1.svg){kind=link}
Hessenberg matrices were first investigated by Karl Hessenberg (1904-1959), a German engineer whose dissertation investigated the computation of eigenvalues and eigenvectors of linear operators.
See also
Hessenberg Decomposition, Toeplitz Matrix, Triangular MatrixPortions of this entry contributed by Austin A. Dubrulle
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References
Hessenberg, K. Thesis. Darmstadt, Germany: Technische Hochschule, 1942.Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. "Reduction of a General Matrix to Hessenberg Form." §11.5 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 476-480, 1992.Referenced on Wolfram|Alpha
Hessenberg MatrixCite this as:
Dubrulle, Austin A. and Weisstein, Eric W. "Hessenberg Matrix." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HessenbergMatrix.html