Let an expression $X^T AX+B^TX$, how can I transform it as $Y^T C Y$; where $Y=[X, 1]$, find $C$ in terms of $A$ and $B$ using Mathematica?

  • $\begingroup$ $C=A+(X^t)^{-1}B^t$? $\endgroup$ – AccidentalFourierTransform Jul 1 at 12:44
  • $\begingroup$ C will be only in term of A and B. $\endgroup$ – user199 Jul 1 at 13:11
  • $\begingroup$ Impossible. Your first expression has non-zero derivative at X=0, while your second does not. They are not equal, unless $C=C(X)$. $\endgroup$ – AccidentalFourierTransform Jul 1 at 13:13
  • $\begingroup$ @AccidentalFourierTransform edited. $\endgroup$ – user199 Jul 1 at 13:41
  • 1
    $\begingroup$ $$C=\begin{pmatrix}A&\frac12B\\\frac12B^t&0\end{pmatrix}?$$ $\endgroup$ – AccidentalFourierTransform Jul 1 at 14:08

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