Let
(1)
| |||
(2)
|
where and are matrices. Then
(3)
|
The proof follows from equating determinants on the two sides of the block matrices
(4)
|
where is the identity matrix and is the zero matrix.
Let
(1)
| |||
(2)
|
where and are matrices. Then
(3)
|
The proof follows from equating determinants on the two sides of the block matrices
(4)
|
where is the identity matrix and is the zero matrix.
Weisstein, Eric W. "Jacobi's Determinant Identity." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/JacobisDeterminantIdentity.html