Citation for block matrix determinant formulae. Proof. The matrix is invertible if and only if When it is invertible, its inverse is. The determinant of a matrix is a special number that can be calculated from a square matrix. A Matrix is an array of numbers: A Matrix (This one has 2 Rows and 2 Columns) The determinant of that matrix is (calculations are explained later): 3×6 − 8×4 = 18 − 32 = −14. I was kind of able to understand this proof on wiki right up until the moment where we go from $\det(I + (A^{-1}u)v^T)$ to the multiplier in question. Determinant of a Matrix. ... Determinant of block matrix as determinant of smaller matrix. Rank one updates to the identity matrix. 1. 0. 0. Alternative proofs Matrix Determinant Lemma. Relating the determinant of block matrix to its inverse. Hot Network Questions Address on a Personal Check Let us first prove the "if" part. The first inversion lemma we present is for rank one updates to identity matrices. The Matrix determinant lemma states that $\det(A + uv^T) = det(A)(1 + v^T(A^{-1}u))$ However, I do not understand how do we get the second multiplier here. Block matrices determinant - What am I missing? 3. Related. 멱영행렬(nilpotent matrix)과 고윳값(eigenvalue) 사이의 관계 (August 18, 2018) 반대칭행렬(skew-symmetric matrix)의 행렬식(determinant) (April 12, 2018) 셔먼-모리슨-우드버리 공식(Sherman–Morrison-Woodbury formula) (August 31, 2017) 행렬식 보조정리(Matrix Determinant Lemma) (August 31, 2017) Proposition Let be the identity matrix and and two column vectors.