• 제목/요약/키워드: Kronecker products of matrices

검색결과 9건 처리시간 0.019초

A SIMPLE METHOD FOR OBTAINING PROJECTION MATRIX USING ALGEBRAIC PROPERTIES

  • Hasik, Sun-Woo
    • Journal of applied mathematics & informatics
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    • 제8권2호
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    • pp.651-658
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    • 2001
  • The projection matrix plays an important role in the linear model theory. In this paper we derive an algebraic relationship between the projection matrices of submatrices of the design matrix. Using this relationship we can easily obtain the projection matrices of any submatrices of the design matrix. Also we show that every projection matrix can be obtained as a linear combination of Kronecker products of identity matrices and matrices with all elements equal to 1.

단순한 메트릭스 계승접근에 의한 고속 아다마르 변환 (A Simple Matrix Factorization Approach to Fast Hadamard Transform)

  • Lee, Moon-Ho
    • 대한전자공학회논문지
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    • 제24권1호
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    • pp.173-176
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    • 1987
  • This paper presents a simple factorization of the Hadamard matrix which is used to develop a fast algorithm for the Hadamard transform. This matrix decomposition is of the kronecker products of identity matrices and successively lower order Hadamard matrices. This following shows how the Kronecker product can be mathematically defined and efficiently implemented using a factorization matrix methods.

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TWO INEQUALITIES INVOLVING HADAMARD PRODUCTS OF POSITIVE SEMI-DEFINITE HERMITIAN MATRICES

  • Cao, Chong-Guang;Yang, Zhong-Peng;Xian Zhang
    • Journal of applied mathematics & informatics
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    • 제10권1_2호
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    • pp.101-109
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    • 2002
  • We extend two inequalities involving Hadamard Products of Positive definite Hermitian matrices to positive semi-definite Hermitian matrices. Simultaneously, we also show the sufficient conditions for equalities to hold. Moreover, some other matrix inequalities are also obtained. Our results and methods we different from those which are obtained by S. Liu in [J. Math. Anal. Appl. 243:458-463(2000)] and B.-Y Wang et al in [Lin. Alg. Appl. 302-303: 163-172(1999)] .

INEQUALITIES INVOLVING KHATRI-RAO PRODUCTS OF HERMITIAN MATRICES

  • Yang, Zhong-Peng;Zhang, Xian;Cao, Chong-Guang
    • Journal of applied mathematics & informatics
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    • 제9권1호
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    • pp.125-133
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    • 2002
  • Recently, Several inequalities Khatri-Rao Products of two four partitioned blocks positive definite real symmetry matrices are established by Liu in[Lin. Alg. Appl. 289(1999): 267-277]. We extend these results in two ways. First, the results are extended to two any partitioned blocks Hermitian matrices. Second, necessary and sufficient conditions under which these inequalities become equalities are presented.

ON THE BOUNDS FOR THE SPECTRAL NORMS OF GEOMETRIC AND R-CIRCULANT MATRICES WITH BI-PERIODIC JACOBSTHAL NUMBERS

  • UYGUN, SUKRAN;AYTAR, HULYA
    • Journal of applied mathematics & informatics
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    • 제38권1_2호
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    • pp.99-112
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    • 2020
  • The study is about the bounds of the spectral norms of r-circulant and geometric circulant matrices with the sequences called biperiodic Jacobsthal numbers. Then we give bounds for the spectral norms of Kronecker and Hadamard products of these r-circulant matrices and geometric circulant matrices. The eigenvalues and determinant of r-circulant matrices with the bi-periodic Jacobsthal numbers are obtained.

직교함수에 의한 쌍일차계의 해석 및 상태 추정에 관한 연구 (A Study on the Analysis and State Estimation of Bilinear Systems via Orthogonal Functions)

  • 안두수;신재선
    • 대한전기학회논문지
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    • 제39권6호
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    • pp.598-606
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    • 1990
  • Common problems encountered when orthogonal functions are used in system analysis and state estimation are the time consuming process of high order matrix inversion required in finding the Kronecker products and the truncation errors. In this paper, therefore, a method for the analysis of bilinear systems using Walsh, Block pulse, and Haar functions is devised, Then, state estimation of bilinear system is also studied based on single term expansion of orthogonal functions. From the method presented here, when compared to the other conventional methods, we can obtain the results with simpler computation as the number of interval increases, and the results approach the original function faster even at randomly chosen points regardless of the definition of intervals. In addition, this method requires neither the inversion of large matrices on obtaining the expansion coefficients nor the cumbersome procedures in finding Kronecker products. Thus, both the computing time and required memory size can be significantly reduced.

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고속 월쉬 변환을 이용한 쌍일차계의 해석에 관한 연구 (A Study on the Analysis of Bilinear Systems via Fast Walsh Transform)

  • 김태훈;심재선
    • 조명전기설비학회논문지
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    • 제16권1호
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    • pp.85-91
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    • 2002
  • 일반적으로 시스템의 해석에 직교 함수를 이용하는 경우에는 크로네커 곱(Kronecker product)에 의하여 고차 행렬에 대한 역변환이 필요하게 되며, 이로 인하여 많은 연산 시간이 필요하게 된다. 본 연구에서는 이 문제점을 해결하고자 고속 월쉬 변환을 이용하는 방법을 제시하였고, 이렇게 함으로써 크로네커 곱에 의한 다루기 힘든 고차 행렬이나 그에 따르는 행렬들의 계산을 필요없게 함으로써 연산의 부담을 줄일 수 있게 된다. 본 연구에서는 쌍일차계의 해석을 위한 직교 함수의 유한 급수 전개 방법과 고속 월쉬 변환 방법을 비교하여 봄으로써 본 연구에서 제안한 방법의 우수성을 표현하였으며, 시뮬레이션을 통하여 고속 월쉬 변환에 와한 쌍일차계 상태 해석 결과를 표시하였다.

Ternary Codes from Modified Jacket Matrices

  • Jiang, Xueqin;Lee, Moon-Ho;Guo, Ying;Yan, Yier;Latif, Sarker Md. Abdul
    • Journal of Communications and Networks
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    • 제13권1호
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    • pp.12-16
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    • 2011
  • In this paper, we construct two families $C^*_m$ and ${\~{C}}^*_m$ of ternary ($2^m$, $3^m$, $2^{m-1}$ ) and ($2^m$, $3^{m+1}$, $2^{m-1}$ ) codes, for m = 1, 2, 3, ${\cdots}$, derived from the corresponding families of modified ternary Jacket matrices. These codes are close to the Plotkin bound and have a very easy decoding procedure.