The discussion centers on proving the determinant identity for vectors \( u, v \in \mathbb{R}^n \), specifically that \( \text{Det}(I + uv^T) = 1 + v^T u \). This identity is derived from the Matrix Determinant Lemma, which provides a method for calculating the determinant of a rank-one update to an identity matrix. The identity matrix \( I \) is defined as an \( n \times n \) matrix, and the proof hinges on understanding the properties of determinants and matrix operations.
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