Answer by Believer for Determinant of enlarged matrix
Consider small case for $n=2$. You can generalize the process for any $n$.Say we have $A=\begin{pmatrix} a & b \\ c & d\end{pmatrix}$.Then $\bar{A}=\begin{pmatrix} a & 0 & b & 0 \\...
View ArticleAnswer by Matteo for Determinant of enlarged matrix
Note that$$\widetilde{A} = A \otimes I,$$for $\otimes$ the Kronecker product, see https://en.wikipedia.org/wiki/Kronecker_product. The determinant of Kronecker products admits a closed form, which is...
View ArticleDeterminant of enlarged matrix
Let $A$ be the $n\times n$ matrix with entries $A_{ij}$ and consider the enlarged $2n\times 2n$ matrix$$\tilde A=\begin{pmatrix}A_{11} & 0 & A_{12} & 0 & \dots & A_{1n} & 0 \\ 0...
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