Joint Approximate Diagonalization of Symmetric Real Matrices of Order 2

Autores

  • Sônia Cristina Poltroniere UNESP - Universidade Estadual Paulista
  • Edilaine Martins Soler UNESP - Universidade Estadual Paulista
  • Alexys Bruno-Alfonso UNESP - Universidade Estadual Paulista

DOI:

https://doi.org/10.5540/tema.2016.017.01.0113

Palavras-chave:

Joint approximate diagonalisation, eigenvectors, optimisation.

Resumo

The problem of joint approximate diagonalization of symmetric real matrices is addressed. It is reduced to an optimization problem with the restriction that the matrix of the similarity transformation is orthogonal. Analytical solutions are derived for the case of matrices of order 2. The concepts of off-diagonalising vectors, matrix amplitude and partially complementary matrices are introduced. This leads to a geometrical interpretation of the joint approximate diagonalization in terms of eigenvectors and off-diagonalising vectors of the matrices. This should be helpful to deal with numerical and computational procedures involving large matrices.

Biografia do Autor

Sônia Cristina Poltroniere, UNESP - Universidade Estadual Paulista

Depto de Matemática

Área: Matemática Aplicada - Pesquisa Operacional

Edilaine Martins Soler, UNESP - Universidade Estadual Paulista

Departamento de Matemática, Faculdade de Ciências

Alexys Bruno-Alfonso, UNESP - Universidade Estadual Paulista

Departamento de Matemática, Faculdade de Ciências

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Publicado

2016-04-29

Como Citar

Poltroniere, S. C., Soler, E. M., & Bruno-Alfonso, A. (2016). Joint Approximate Diagonalization of Symmetric Real Matrices of Order 2. Trends in Computational and Applied Mathematics, 17(1), 113. https://doi.org/10.5540/tema.2016.017.01.0113

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