Jacket matrix information

In mathematics, a jacket matrix is a square symmetric matrix $A=(a_{ij})$ of order n if its entries are non-zero and real, complex, or from a finite field, and

\ AB=BA=I_{n}

where I_n is the identity matrix, and

\ B={1 \over n}(a_{ij}^{-1})^{T}.

where T denotes the transpose of the matrix.

In other words, the inverse of a jacket matrix is determined by its element-wise or block-wise inverse. The definition above may also be expressed as:

\forall u,v\in \{1,2,\dots ,n\}:~a_{iu},a_{iv}\neq 0,~~~~\sum _{i=1}^{n}a_{iu}^{-1}\,a_{iv}={\begin{cases}n,&u=v\\0,&u\neq v\end{cases}}

The jacket matrix is a generalization of the Hadamard matrix; it is a diagonal block-wise inverse matrix.

Jacket matrix information

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