Computing the determinant of a block matrix
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I am having trouble using a well-known formula for computing the determinant of a block matrix. That is, if
in which A and D are square matrices and exists then
The code snippet below should achieve this but it returns two different results. I'm sure it's a very trivial mistake I've made but I've probably been staring at it too long now to find it.
As a follow up, does anyone know if there is a suitably adjusted version of this formula for the case when it is B and C which are the square matrices?
function [detM,detBlock] = BlockDeterminant()
M = magic(4);
detM = det(M);
A = M(1:3,1:3);
B = M(1:3,4);
C = M(4,1:3);
D = M(4,4);
detBlock = det(A)*det(D-C*inv(A)*B);