Quadratische Formen nebst Anwendungen

Rudolf Zurmühl

Chapter III. Kapitel in Matrizen, 1958, pp 129-149 from Springer

Abstract: Zusammenfassung Unter einer reellen quadratischen Form in n reellen Veränderlichen x1, x2, ... , xn versteht man einen in den xi homogenen Ausdruck zweiten Grades mit reellen Koeffizienten a ik (1’) $$\left. \begin{gathered}Q = {a_{11}}x_1^2 + 2{a_{12}}{x_1}{x_2} + ... + 2{a_{1n}}{x_1}{x_n} \hfill \\+ {a_{22}}x_2^2 + ... + 2{a_{2n}}{x_2}{x_n} \hfill \\+ ............................... \hfill \\+ {a_{nn}}x_n^2. \hfill \\\end{gathered} \right\}$$ Setzen wir überdies a ik = a ki , so läßt sich dies so schreiben: (1’’) $$\left. \begin{gathered}Q = {a_{11}}x_1^2 + 2{a_{12}}{x_1}{x_2} + ... + 2{a_{1n}}{x_1}{x_n} \hfill \\+ {a_{22}}x_2^2 + ... + 2{a_{2n}}{x_2}{x_n} \hfill \\+ ............................... \hfill \\+ {a_{nn}}x_n^2. \hfill \\\end{gathered} \right\}$$ .

Date: 1958
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DOI: 10.1007/978-3-642-53291-7_3

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