• Title/Summary/Keyword: Orthogonal Matrix

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Comparison of Algebraic design methodologies for Unknown Inputs Observer via Orthogonal Functions (대수적 미지입력관측기 설계를 위한 직교함수의 응용)

  • Ahn, P.;Lee, S.J.;Kim, H.W.
    • Proceedings of the KIEE Conference
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    • 2005.07d
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    • pp.2543-2545
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    • 2005
  • It is well known that the orthogonal function is a very useful to estimate an unknown inputs in the linear dynamic systems for its recursive algebraic algorithm. At this aspects, derivative operation(matrix) of orthogonal functions(walsh, block pulse and haar) are introduced and shown how it can useful to design an UIO(unknown inputs observer) design.

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A Syndrome-distribution decoding MOLS L$_{p}$ codes

  • Hahn, S.;Kim, D.G.;Kim, Y.S.
    • Communications of Mathematical Education
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    • v.6
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    • pp.371-381
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    • 1997
  • Let p be an odd prime number. We introduce simple and useful decoding algorithm for orthogonal Latin square codes of order p. Let H be the parity check matrix of orthogonal Latin square code. For any x ${\in}$ GF(p)$^{n}$, we call xH$^{T}$ the syndrome of x. This method is based on the syndrome decoding for linear codes. In L$_{p}$, we need to find the first and the second coordinates of codeword in order to correct the errored received vector.

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A Study on Image Data Compression by using Hadamard Transform (Hadamard변환을 이용한 영상신호의 전송량 압축에 관한 연구)

  • 박주용;이문호;김동용;이광재
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.11 no.4
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    • pp.251-258
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    • 1986
  • There is much redundancy in image data such as TV signals and many techniques to redice it have been studied. In this paper, Hadamard transform is studied through computer simulation and experimental model. Each element of hadamard matrix is either +1 or -1, and the row vectors are orthogonal to another. Its hardware implementation is the simplest of the usual orthogonal transforms because addition and sulbraction are necessary to calculate transformed signals, while not only addition but multiplication are necessary in digital Fourier transform, etc. Linclon data (64$ imes$64) are simulated using 8th-order and 16th-order Hadamard transform, and 8th-order is implemented to hardware. Theoretical calculation and experimental result of 8th-order show that 2.0 bits/sample are required for good quality.

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SIGN PATTERNS OF IDEMPOTENT MATRICES

  • Hall, Frank J.;Li, Zhong-Shan
    • Journal of the Korean Mathematical Society
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    • v.36 no.3
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    • pp.469-487
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    • 1999
  • Sign patterns of idempotent matrices, especially symmetric idempotent matrices, are investigated. A number of fundamental results are given and various constructions are presented. The sign patterns of symmetric idempotent matrices through order 5 are determined. Some open questions are also given.

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A New Aspect of Comrade Matrices by Reachability Matrices

  • Solary, Maryam Shams
    • Kyungpook Mathematical Journal
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    • v.59 no.3
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    • pp.505-513
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    • 2019
  • In this paper, we study orthanogonal polynomials by looking at their comrade matrices and reachability matrices. First, we focus on the algebraic structure that is exhibited by comrade matrices. Then, we explain some properties of this algebraic structure which helps us to find a connection between comrade matrices and reachability matrices. In the last section, we use this connection to determine the determinant, eigenvalues, and eigenvectors of these matrices. Finally, we derive a factorization for det R(A, x), where R(A, x) is the reachability matrix for a comrade matrix A and x is a vector of indeterminates.

Orthogonal Integer Transform (직교 정수형 변환)

  • 이종하;곽훈성
    • Journal of the Korean Institute of Telematics and Electronics B
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    • v.31B no.1
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    • pp.64-71
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    • 1994
  • In this paper, we propose orthogonal integer transform(OIT) with general form. Considering the orthogonality and magnitude value order of the DCT Matrix whose performance is found to be close to that of the KLT, known to be optimal. The proposed OIT matrix is composed of values minimizing Hibert-Schmidt norm among integer values which satisfy the condition of orthogonality and the relative magnitudes of the DCT matrix. Comparing the OIT with the DCT, CMT, and ICT in error characteristics, transform efficiency, and maximum reducible bit, it is shown that the performance of the OIT compares more closely to that of the KLT relative to the performances of the DCT, CMT, and ICT when N=8.

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Numerical Simulation of 2-D Estuaries and Coast by Multi-Domain and the Interpolating Matrix Method (Multi-Domain과 행렬 보간법을 이용한 강 하구와 연안의 2차원 수치해석)

  • Chae H. S.
    • Journal of computational fluids engineering
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    • v.2 no.1
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    • pp.21-28
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    • 1997
  • This paper presents a two-dimensional horizontal implicit model to general circulation in estuaries and coastal seas. The model is developed in non-orthogonal curvilinear coordinates system, using the Interpolating Matrix Method (IMM), in combination with a technique of multi-domain. In the propose model, the Saint-Venant equations are solved by a splitting-up technique, in the successive steps; convection, diffusion and wave propagation. The ability of the proposed model to deal with full scale nature is illustrated by the interpretation of a dye-tracing experiment in the Gironde estuary.

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ON DIFFERENTIABILITY OF THE MATRIX TRACE OPERATOR AND ITS APPLICATIONS

  • Dulov, E.V.;Andrianova, N.A.
    • Journal of applied mathematics & informatics
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    • v.8 no.1
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    • pp.97-109
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    • 2001
  • This article is devoted to “forgotten” and rarely used technique of matrix analysis, introduced in 60-70th and enhanced by authors. We will study the matrix trace operator and it’s differentiability. This idea generalizes the notion of scalar derivative for matrix computations. The list of the most common derivatives is given at the end of the article. Additionally we point out a close connection of this technique with a least square problem in it’s classical and generalized case.

COMPUTATION OF HANKEL MATRICES IN TERMS OF CLASSICAL KERNEL FUNCTIONS IN POTENTIAL THEORY

  • Chung, Young-Bok
    • Journal of the Korean Mathematical Society
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    • v.57 no.4
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    • pp.973-986
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    • 2020
  • In this paper, we compute the Hankel matrix representation of the Hankel operator on the Hardy space of a general bounded domain with respect to special orthonormal bases for the Hardy space and its orthogonal complement. Moreover we obtain the compact form of the Hankel matrix for the unit disc case with respect to these bases. One can see that the Hankel matrix generated by this computation turns out to be a generalization of the case of the unit disc from the single simply connected domain to multiply connected domains with much diversities of bases.

AN ELEMENTARY COMPUTATION OF HANKEL MATRICES ON THE UNIT DISC

  • Chung, Young-Bok
    • Honam Mathematical Journal
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    • v.43 no.4
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    • pp.691-700
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    • 2021
  • In this paper, we compute directly the Hankel matrix representation of the Hankel operator on the Hardy space of the unit disc without using any classical kernel functions with respect to special orthonormal bases for the Hardy space and its orthogonal complement. This gives an elementary proof for the formula.