scholarly journals Sign patterns of J-orthogonal matrices

2017 ◽  
Vol 5 (1) ◽  
pp. 225-241
Author(s):  
Frank J. Hall ◽  
Zhongshan Li ◽  
Caroline T. Parnass ◽  
Miroslav Rozložník
Keyword(s):  
Orthogonal Matrix ◽  
Orthogonal Matrices ◽  
Sign Patterns ◽  
Exchange Operator ◽  
Czechoslovak Math ◽  
Siam Review ◽  
G Matrices ◽  
Block Diagonal

Abstract This paper builds upon the results in the article “G-matrices, J-orthogonal matrices, and their sign patterns", Czechoslovak Math. J. 66 (2016), 653-670, by Hall and Rozloznik. A number of further general results on the sign patterns of the J-orthogonal matrices are proved. Properties of block diagonal matrices and their sign patterns are examined. It is shown that all 4 × 4 full sign patterns allow J-orthogonality. Important tools in this analysis are Theorem 2.2 on the exchange operator and Theorem 3.2 on the characterization of J-orthogonal matrices in the paper “J-orthogonal matrices: properties and generation", SIAM Review 45 (3) (2003), 504-519, by Higham. As a result, it follows that for n ≤4 all n×n full sign patterns allow a J-orthogonal matrix as well as a G-matrix. In addition, the 3 × 3 sign patterns of the J-orthogonal matrices which have zero entries are characterized.

Some Properties of the Exchange Operator with respect to Structured Matrices defined by Indefinite Scalar Product Spaces

2015 ◽  
Vol 30 ◽  
Author(s):  
Hanz Martin Cheng ◽  
Roden Jason David
Keyword(s):  
Scalar Product ◽  
Structured Matrices ◽  
Product Spaces ◽  
Orthogonal Matrices ◽  
Structured Matrix ◽  
Exchange Operator ◽  
Siam Review

The properties of the exchange operator on some types of matrices are explored in this paper. In particular, the properties of exc(A,p,q), where A is a given structured matrix of size (p+q)×(p+q) and exc : M ×N×N → M is the exchange operator are studied. This paper is a generalization of one of the results in [N.J. Higham. J-orthogonal matrices: Properties and generation. SIAM Review, 45:504–519, 2003.].

scholarly journals G-matrices, J-orthogonal matrices, and their sign patterns

2016 ◽  
Vol 66 (3) ◽  
pp. 653-670 ◽  
Author(s):  
Frank J. Hall ◽  
Miroslav Rozložník
Keyword(s):  
Orthogonal Matrices ◽  
Sign Patterns ◽  
G Matrices

scholarly journals ROTATION MATRIX SAMPLING SCHEME FOR MULTIDIMENSIONAL PROBABILITY DISTRIBUTION TRANSFER

2016 ◽  
Vol III-7 ◽  
pp. 103-110
Author(s):  
P. Srestasathiern ◽  
S. Lawawirojwong ◽  
R. Suwantong ◽  
P Phuthong
Keyword(s):  
Probability Distribution ◽  
Orthogonal Matrix ◽  
Rotation Matrix ◽  
Sampling Scheme ◽  
Uniform Rotation ◽  
Householder Transformation ◽  
Orthogonal Matrices ◽  
Matrix Sampling ◽  
Paper Address ◽  
Multidimensional Probability

This paper address the problem of rotation matrix sampling used for multidimensional probability distribution transfer. The distribution transfer has many applications in remote sensing and image processing such as color adjustment for image mosaicing, image classification, and change detection. The sampling begins with generating a set of random orthogonal matrix samples by Householder transformation technique. The advantage of using the Householder transformation for generating the set of orthogonal matrices is the uniform distribution of the orthogonal matrix samples. The obtained orthogonal matrices are then converted to proper rotation matrices. The performance of using the proposed rotation matrix sampling scheme was tested against the uniform rotation angle sampling. The applications of the proposed method were also demonstrated using two applications i.e., image to image probability distribution transfer and data Gaussianization.

Inverse problems for multidimensional vibrating systems

1992 ◽  
Vol 439 (1907) ◽  
pp. 511-530 ◽  
Keyword(s):  
Frequency Response ◽  
Stiffness Matrix ◽  
Jacobi Matrix ◽  
Dynamic Stiffness ◽  
Orthogonal Matrix ◽  
Generalized Coordinates ◽  
Response Data ◽  
Special Information ◽  
Vibrating Systems ◽  
Block Diagonal

Many vibrating systems involve interactions only between neighbouring parts of the system. Frequently, such systems are analysed by supposing that the mass distribution is lumped at the generalized coordinates. Undamped systems of this type involve a block tri-diagonal stiffness matrix K and a block diagonal inertia matrix M . The inverse problem is to reconstruct K and M from frequency response data. The known reconstruction of a Jacobi matrix using the Forsythe algorithm is generalized so that a block Jacobi matrix can be reconstructed from a certain spectral function. This analysis is used to construct the dynamic stiffness matrix A = L -1 KL -T ( M = LL T ) from the frequency response; A is determined to within a block diagonal orthogonal matrix. It is shown that K and M can be separated by using special information about their forms. A vibrating lattice composed of rods and masses is used as an example.

scholarly journals Functions Preserving Orthogonality of Hermitian Matrices

2021 ◽  
Vol 13 (4) ◽  
pp. 77
Author(s):  
Meili Liu ◽  
Liwei Wang ◽  
Chun-Te Lee ◽  
Jeng-Eng Lin
Keyword(s):  
Symmetric Matrices ◽  
Hermitian Matrices ◽  
Orthogonal Matrices ◽  
Triangular Matrices ◽  
Upper Triangular Matrices

Inspired by the results that functions preserve orthogonality of full matrices, upper triangular matrices, and symmetric matrices. We finish the work by finding special orthogonal matrices which satisfy the conditions of preserving orthogonality functions. We give a characterization of functions preserving orthogonality of Hermitian matrices.

Orthogonal Matrices in Four-Space

1949 ◽  
Vol 1 (1) ◽  
pp. 69-72
Author(s):  
C. C. MacDuffee
Keyword(s):  
Orthogonal Transformation ◽  
Orthogonal Matrix ◽  
Orthogonal Matrices ◽  
Image Position ◽  
Proper Orthogonal ◽  
The Relationship

Every proper orthogonal matrix A can be writtenwhere Q is a skew matrix [6], and conversely every such matrix A is orthogonal. It is also known that every proper orthogonal transformation in real Euclidean four-space may be characterized in term of quaternions [1, 3] by the equationdetermines with the origin a vector having the coordinates (XQ, XI, x2, x3). The relationship between these two representations was clearly shown by Murnaghan [5].

scholarly journals Characterization of star sign patterns that require Hn

2016 ◽  
Vol 499 ◽  
pp. 43-65 ◽  
Author(s):  
Wei Gao ◽  
Zhongshan Li ◽  
Lihua Zhang
Keyword(s):  
Sign Patterns

scholarly journals Block-diagonal characterization of locally finite simple groups of p-type

2013 ◽  
Vol 16 (4) ◽  
Author(s):  
Stefaan Delcroix
Keyword(s):  
Simple Groups ◽  
Finite Simple Groups ◽  
Locally Finite ◽  
General Family ◽  
P Type ◽  
Block Diagonal

Abstract.In this paper, we prove the following characterization of LFS-groups ofLet(i)(ii) there exists(a)(b)(c) forwhereThenWe use this theorem to construct a general family of LFS-groups of

On completion in the category SSNσFrm

2013 ◽  
Vol 63 (2) ◽  
Author(s):  
Inderasan Naidoo
Keyword(s):  
Similar Construction ◽  
Total Boundedness ◽  
Czechoslovak Math ◽  
Samuel Compactification ◽  
Phd Thesis ◽  
Uniform Frames

AbstractWe introduce the category SSN σ Frm of super strong nearness σ-frames and show the existence of a completion for a super strong nearness σ-frame unique up to isomorphism by the similar construction presented in [WALTERS-WAYLAND, J. L.: Completeness and Nearly Fine Uniform Frames. PhD Thesis, Univ. Catholique de Louvain, 1996] and [WALTERS-WAYLAND, J. L.: A Shirota Theorem for frames, Appl. Categ. Structures 7 (1999), 271–277]. Completion is also shown to be a coreflection in SSN σ Frm. We also engage with the notion of total boundedness for nearness σ-frames and provide a characterization of the Samuel compactification of a nearness σ-frame alternative to the description in [NAIDOO, I.: Samuel compactification and uniform coreflection of nearness σ-frames, Czechoslovak Math. J. 56(131) (2006), 1229–1241].

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