Let $A_1, A_2, \ldots, A_k$ be square upper-triangular matrices with non-zero determinants $D_1, D_2, \ldots, D_k$. What is the volume of the parallelepiped defined by the columns of the matrix below? $$B = \begin{pmatrix} A_1 \\ A_2 \\ \vdots \\ A_k \end{pmatrix}$$ Equivalently, what is the value of $\sqrt{\det(B^T B)}$?
2026-03-26 12:52:51.1774529571
Volume of parallelepiped formed by stacking diagonal matrices
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