Quadratic Forms and Transformation Let \(A = \{a_{ij}\}\) be an \(n\times n\) matrix. A quadratic function of \(n\) variables \(x = (x_1,\ldots, x_n)’\) is defined as \[ f(x) = x' A x = \sum_{i,j} a_{ij} x_i x_j. \] Without loss…

Quadratic Forms and Transformation Let \(A = \{a_{ij}\}\) be an \(n\times n\) matrix. A quadratic function of \(n\) variables \(x = (x_1,\ldots, x_n)’\) is defined as \[ f(x) = x' A x = \sum_{i,j} a_{ij} x_i x_j. \] Without loss…