evlyn said:That helped.
So now using the definition (usually a good thing) I have:
(AB)^+_ij = [AB_ji]^* = A_ji ^* B_ji^* = B_ij^+ A_ij^+ = B^+ A^+
I know that the complex conjugate is distributive can I just assume that for the proof?
The Hermitian identity for matrix multiplication states that the conjugate transpose of the product of two matrices is equal to the product of their individual conjugate transposes in reverse order.
The Hermitian identity is used to simplify complex matrix calculations, particularly in the context of linear algebra. It allows for the manipulation of matrix equations by taking advantage of properties such as commutativity and associativity.
A Hermitian matrix is a square matrix that is equal to its own conjugate transpose. This means that the matrix is symmetric across its diagonal, with real values on the diagonal and complex conjugate values on the off-diagonal. A non-Hermitian matrix does not have this property and can have any arrangement of real and complex values.
Yes, the Hermitian identity can be extended to any number of matrices. In this case, the conjugate transpose of the product of the matrices will be equal to the product of their individual conjugate transposes in reverse order.
The Hermitian identity is closely related to the concept of adjoint matrices. In fact, the Hermitian identity can be seen as a special case of the more general adjoint identity, which states that the adjoint of the product of two matrices is equal to the product of their individual adjoints in reverse order.