Suppose $X_1,X_2,X_3\in\mathbb R^{2\times1}$. Then $$ \det[ X_1,X_2] +\det[X_2,X_3] + \det[X_3,X_1] = \det[X_2-X_1,X_3-X_1]. $$ Where are this identity and higher-dimensional versions and their proofs found?
2026-04-03 03:16:10.1775186170
Reference request on a sum-of-determinants identity
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