In mathematics, a jacket matrix is a square matrix of order n if its entries are non-zero and real, complex, or from a finite field, and
Hierarchy of matrix types
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.
||.... -2, -1, 0 1, 2,.....
||.... 1, 2, 4,.....
As shown in Table, i.e. in series, n=2 case, Forward: , Inverse : , then, .
Therefore, exist an element-wise inverse.
or more general
For m x m matrices,
denotes an mn x mn block diagonal Jacket matrix.
- Moon Ho Lee,The Center Weighted Hadamard Transform, IEEE Transactions on Circuits Syst. Vol. 36, No. 9, PP. 1247–1249, Sept.1989.
- K.J. Horadam, Hadamard Matrices and Their Applications, Princeton University Press, UK, Chapter 4.5.1: The jacket matrix construction, PP. 85–91, 2007.
- Moon Ho Lee, Jacket Matrices: Constructions and Its Applications for Fast Cooperative Wireless Signal Processing,LAP LAMBERT Publishing, Germany,Nov. 2012.