• Title/Summary/Keyword: Equivalent Hadamard matrix

Search Result 4, Processing Time 0.023 seconds

Equivalence of Hadamard Matrices Whose Rows Form a Vector Space (행백터 집합이 벡터공간을 이루는 하다마드 행렬의 동치관계)

  • Jin, Seok-Yong;Kim, Jeong-Heon;Park, Ki-Hyeon;Song, Hong-Yeop
    • The Journal of Korean Institute of Communications and Information Sciences
    • /
    • v.34 no.7C
    • /
    • pp.635-639
    • /
    • 2009
  • In this paper, we show that any two Hadamard matrices of the same size are equivalent if they have the property that the rows of each Hadamard matrix are closed under binary vector addition. One of direct consequences of this result is that the equivalence between cyclic Hadamard matrices constructed by maximal length sequences and Walsh-Hadamard matrix of the same size generated by Kronecker product can be established.

Eigenvalues of Non-Sylvester Hadamard Matrices Constructed by Monomial Permutation Matrices (단항순열행렬에 의해 구성된 비실베스터 하다마드 행렬의 고유치)

  • Lee Seung-Rae;No Jong-Seon;Sung Koeng-Mo
    • The Journal of Korean Institute of Communications and Information Sciences
    • /
    • v.31 no.4C
    • /
    • pp.434-440
    • /
    • 2006
  • In this paper, the eigenvalues of various non-Sylvester Hadamard matrices constructed by monomial permutation matrices are derived, which shows the relation between the eigenvalues of the newly constructed matrix and Sylvester Hadamard matrix.

REAL SOLUTIONS OF THE EQUATION (equation omitted)

  • Yang, Zhong-Peng;Cao, Chong-Gu;Tang, Xiao-Min
    • Journal of applied mathematics & informatics
    • /
    • v.13 no.1_2
    • /
    • pp.117-123
    • /
    • 2003
  • For an n ${\times}$ n real matrix X, let ${\Phi}$(X) = X o (X$\^$-1/)$\^$T/, where o stands for the Hadamard (entrywise) product. Suppose A, B, G and D are n ${\times}$ n real nonsingular matrices, and among them there are at least one solutions to the equation (equation omitted). An equivalent condition which enable (equation omitted) become a real solution ot the equation (equation omitted), is given. As application, we get new real solutions to the matrix equation (equation omitted) by applying the results of Zhang. Yang and Cao [SIAM.J.Matrix Anal.Appl, 21(1999), pp: 642-645] and Chen [SIAM.J.Matrix Anal.Appl, 22(2001), pp:965-970]. At the same time, all solutions of the matrix equation (equation omitted) are also given.

A Study on Phase-Multiplexed Volume Hologram using Spatial Light Modulator (공간광변조기를 이용한 위상다중화 체적 홀로그램에 관한 연구)

  • Jo, Jong-Dug;Kim, Kyu-Tae
    • 전자공학회논문지 IE
    • /
    • v.44 no.3
    • /
    • pp.23-34
    • /
    • 2007
  • For an effective phase multiplexing in a volume holographic system, four types of phase code, pseudo random code(PSC), Hadamard matrix(HAM), pure random code(PRC), equivalent random code(ERC), used as reference beams are generated. In case of $32{\times}32$ address beam, a phase error with 0%, 5%, 10%, 15%, 20%, and 25% error rate, is purposely added to the real phase values in order to consider the practical SLM's nonlinear characteristics of phase modulation in computer simulation. Crosstalks and SNRs(signal-to-ratio) are comparatively analyzed for these phase codes by the auto-correlation and cross-correlation. PSC has the lowest cross-correlation mean value of 0.067 among four types of phase code, which means the SNR of the pseudo random phase code is higher than other phase codes. Also, the standard deviation of the pseudo random phase code indicating the degree of recalled data degradation is the lowest value of 0.0113. In order to analyze the affect by variation of pixel size, simulation is carried out by same method for the case of $32{\times}32$, $64{\times}64$, $128{\times}128$, $256{\times}256$ address beams.