Physical significance of taking hermitian of a matrix

[ABIJOHN]

What is the physical significance of taking hermitian of a matrix?

 

[ckshivaram]

check these discussion
hermitian matrices
**broken link removed**

 

[sapna.dudani@gmail.com]

In mathematics, a Hermitian matrix (or self-adjoint matrix) is a square matrix with complex entries that is equal to its own conjugate transpose – that is, the element in the i-th row and j-th column is equal to the complex conjugate of the element in the j-th row and i-th column, for all indices i and j:
Hermitian matrices can be understood as the complex extension of real symmetric matrices.
In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose.
The entries of a symmetric matrix are symmetric with respect to the main diagonal (top left to bottom right). So if the entries are written as A = (aij), then

Every diagonal matrix is symmetric, since all off-diagonal entries are zero. Similarly, each diagonal element of a skew-symmetric matrix must be zero, since each is its own negative.
In linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space. The corresponding object for a complex inner product space is a Hermitian matrix with complex-valued entries, which is equal to its conjugate transpose. Therefore, in linear algebra over the complex numbers, it is often assumed that a symmetric matrix refers to one which has real-valued entries. Symmetric matrices appear naturally in a variety of applications, and typical numerical linear algebra software makes special accommodations for them.

Matrices make a great tool to design a comprehensive assessment. When matrices are used in assessment, they provide a much more in depth look at not just the assessment, but the depth and complexity too.