User:Leejacket
In mathematics, a jacket matrix is a square matrix of order n whose entries are non-zero and from a field,( including real field, complex field, or finite field ) if
where In is the identity matrix, and
where T denotes the transpose of the matrix.
Properties
[edit]![](http://upload.wikimedia.org/wikipedia/commons/7/74/Had_otr_jac.png)
The jacket matrix is a generalization of the Hadamard matrix. The most important property of a jacket matrix is that its inverse may be determined by its element-wise or block-wise inverse.
There are three main classes of matrices :
3.Jacket matrices:
Example
[edit]or more general
References
[edit]- M.H. Lee, The Center Weighted Hadamard Transform, IEEE Trans.1989 CAS-36, (9), pp.1247-1249.
- M.H. Lee, A New Reverse Jacket Transform and its Fast Algorithm, IEEE Trans. Circuits Syst.-II , vol 47, pp.39-46, 2000.
- M.H. Lee and B.S. Rajan, A Generalized Reverse Jacket Transform, IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., vol. 48 no.7 pp 684-691, 2001.
- J. Hou, M.H. Lee and J.Y. Park, New Polynomial Construction of Jacket Transform, IEICE Trans. Fundamentals, vol. E86-A no. 3, pp.652-659, 2003.
- W.P. Ma and M. H. Lee, Fast reverse Jacket Transform Algorithms, Electronics Letter, vol. 39 no. 18 , 2003.
- 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.
External links
[edit]Human Nose Morphology and Air Humidity
[edit]Human Nose height and width will vary based on air humidity. In Australia Cairns there is a tree called Strangler Fig. A base of the tree is shaped to maximize an absorption of a moisture and resembles a human nose. By comparing morphology of a nose of Asians against Europeans and Americans, one can see that they noticeably differ from each other: Asians’ noses are statistically smaller.
Asian & Korean Europe & Americans
Humidity 66.8 % ≈ 30%
Nose (30 years old) Height ≈ 2 cm Height ≈ 2.6 cm
Length ≈ 5 cm Length ≈ 5.8 cm
One of the consequences of race-dependent nose morphology is a presence of a substantial amount of strong nasal phones in European languages. To compensate for a low-moisture level, Europeans and Americans tend to drink lots of coffee and beer …
References:
1. United Kingdom, Independent News Paper, 27 Aug 2002.
2. Moon Ho Lee, Goal Gate II, Shina Publications, Korea, 15 July 2006.
E-mail: Professor Moon Ho Lee, moonho@chonbuk.ac.kr