Hessenberg Operator
Hessenberg may refer to: People: *Gerhard Hessenberg (1874–1925), German mathematician *Karl Hessenberg (1904–1959), German mathematician and engineer *Kurt Hessenberg (1908–1994), German composer and professor at the Hochschule für Musik und Darstellende Kunst in Frankfurt am Main Mathematics: *Hessenberg matrix, one that is "almost" triangular *Hessenberg variety In geometry, Hessenberg varieties, first studied by Filippo De Mari, Claudio Procesi, and Mark A. Shayman, are a family of subvarieties of the full flag variety which are defined by a Hessenberg function ''h'' and a linear transformation ''X'' ...

Gerhard Hessenberg
Gerhard Hessenberg (16 August 1874 – 16 November 1925) was a German mathematician who worked in projective geometry, differential geometry, and set theory. Career Hessenberg received his Ph.D. from the University of Berlin in 1899 under the guidance of Hermann Schwarz and Lazarus Fuchs. His name is usually associated with projective geometry, where he is known for proving that Desargues' theorem is a consequence of Pappus's hexagon theorem, and differential geometry where he is known for introducing the concept of a connection. He was also a set theorist: the Hessenberg sum and product of ordinals are named after him. However, Hessenberg matrices are named for Karl Hessenberg, a near relative. In 1908 Gerhard Hessenberg was an Invited Speaker of the International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Un ...
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Karl Hessenberg
Karl Adolf Hessenberg (September 8, 1904 – February 22, 1959) was a German mathematician and engineer. The Hessenberg matrix form is named after him. Education From 1925 to 1930 he studied electrical engineering at the Technische Hochschule Darmstadt (today Technische Universität Darmstadt) and graduated with a diploma. From 1931 to 1932 he was an assistant to Alwin Walther at the Technische Hochschule Darmstadt, afterwards he worked at the power station in Worms, Germany. From 1936 he worked as an engineer at AEG, first in Berlin and later in Frankfurt. In 1940 he received his PhD from Alwin Walther at the Technische Hochschule in Darmstadt. Family Hessenberg was also the brother of composer Kurt Hessenberg, and the great-grandson of doctor and author Heinrich Hoffmann. The Hessenberg sum and product of ordinals are named after Gerhard Hessenberg Gerhard Hessenberg (16 August 1874 – 16 November 1925) was a German mathematician who worked in projective geometry, d ...
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Kurt Hessenberg
Kurt Hessenberg (17 August 1908 – 17 June 1994) was a German composer and professor at the Hochschule für Musik und Darstellende Kunst in Frankfurt. Life Kurt Hessenberg was born on 17 August 1908 in Frankfurt, as the fourth and last child of the lawyer Eduard Hessenberg and his wife Emma, née Kugler. Among his ancestors was Heinrich Hoffmann, whose famous children's book ''Struwwelpeter'' Hessenberg was to arrange for children's choir (op. 49) later in his life. From 1927–1931 Hessenberg studied at the Leipzig Conservatory. Among his teachers were Günter Raphael (composition) and Robert Teichmüller (piano). In 1933 Hessenberg became a teacher at the Hoch'sche Konservatorium in Frankfurt am Main, where he himself had taken his earliest music lessons. In 1940 Hessenberg received the "Nationaler Kompositionspreis" (national prize for composition), joined the NSDAP in 1942, and in 1951 he was awarded the Robert-Schumann-Prize of the city of Düsseldorf for his cantata "V ...
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Hessenberg Matrix
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. Definitions Upper Hessenberg matrix A square n \times n matrix A is said to be in upper Hessenberg form or to be an upper Hessenberg matrix if a_=0 for all i,j with i > j+1. An upper Hessenberg matrix is called unreduced if all subdiagonal entries are nonzero, i.e. if a_ \neq 0 for all i \in \. Lower Hessenberg matrix A square n \times n matrix A is said to be in lower Hessenberg form or to be a lower Hessenberg matrix if its transpose is an upper Hessenberg matrix or equivalently if a_=0 for all i,j with j > i+1. A lower Hessenberg matrix is called unreduced if all superdiagonal entries are nonzero, i.e. if a_ \neq 0 for all i \in \. Examples Consider the following matri ...
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