Mar 12, 2012 Thread starter #1 A Amer Active member Mar 1, 2012 275 \[ \text{Let u,v } \in \mathbb{R}^n \;\; \text{Show that } \;\;, Det(I + uv^T) = 1 + v^T u \] I is the identity matrix nxn any hints ?

\[ \text{Let u,v } \in \mathbb{R}^n \;\; \text{Show that } \;\;, Det(I + uv^T) = 1 + v^T u \] I is the identity matrix nxn any hints ?

Mar 12, 2012 #2 E Evgeny.Makarov Well-known member MHB Math Scholar Jan 30, 2012 2,492 This is a special case of the Matrix determinant lemma.