Jacket matrix
In mathematics, a jacket matrix is a square symmetric matrix of order n if its entries are non-zero and real, complex, or from a finite field, and
where In is the identity matrix, and
where T denotes the transpose of the matrix.
In other words, the inverse of a jacket matrix is determined its element-wise or block-wise inverse. The definition above may also be expressed as:
The jacket matrix is a generalization of the Hadamard matrix,also it is a Diagonal block-wise inverse matrix.Motivation
As shown in Table, i.e. in series, n=2 case,
Forward:, Inverse :, then,.
Therefore, exist an element-wise inverse.Example 1.
or more generalExample 2.
For m x m matrices,
denotes an mn x mn block diagonal Jacket matrix.Example 3.
Euler's Formula:
Therefore,
Also,
,.
Finally,
A·B=B·A=I
