Find the signature of the quadratic form

Question

Find the signature of the quadratic form $x_1^2-2x_2^2+3x_3^2$

14 Feb 2025

Answer :

Word Count : 190

The quadratic form in question is: \[ Q(x) = x_1^2 - 2x_2^2 + 3x_3^2 \] This is a diagonal quadratic form with the following matrix representation: \[ Q(x) = \begin{pmatrix} x_1 & x_2 & x_3 \end{pmatrix} \begin{pmatrix} 1 & 0 & 0 \\ 0 & -2 & ____ __________ ___ ________ ___ __________ _________ _____ ______ ___ ________.
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