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2 | made matrices indefinite | ||
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I suspect that you mean Then the answer in still no under the added condition that both matrices are not of full rank. Consider $$ A_1 = \begin{pmatrix}1 & 0 & 0\\ 0 & 0 & 0\\ 0 & 0\end{pmatrix}\quad 0 & -1\end{pmatrix}\quad A_2 = \begin{pmatrix}0 & 0 & 0\\ 0 & 1 & 0\\ 0 & 1\end{pmatrix}. 0 & -1\end{pmatrix}. $$ |
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I suspect that you mean Then the answer in still no under the added condition that both matrices are not of full rank. Consider $$ A_1 = \begin{pmatrix}1 & 0 \\ 0 & 0\end{pmatrix}\quad A_2 = \begin{pmatrix}0 & 0 \\ 0 & 1\end{pmatrix}. $$ |
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