Spectral properties of the matrix $$C^{-1} B$$ C - 1 B with positive definite $$C$$ C and Hermitian $$B$$ B as well as applications

Author:

Kohaupt L.

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Computational Mathematics

Reference11 articles.

1. Czornik, A., Jurgaś, P.: Some properties of the spectral radius of a set of matrices. Int. J. Appl. Math. Sci. 16(2), 183–188 (2006)

2. Kohaupt, L.: Construction of a biorthogonal system of principal vectors of the matrices $$A$$ A and $$A^{\ast }$$ A * with applications to the initial value problem $$\dot{x}=A\, x, \; x(t_0)=x_0$$ x ˙ = A x , x ( t 0 ) = x 0 . J. Comput. Math. Optim. 3(3), 163–192 (2007)

3. Kohaupt, L.: Biorthogonalization of the principal vectors for the matrices $$A$$ A and $$A^{\ast }$$ A * with application to the computation of the explicit representation of the solution $$x(t)$$ x ( t ) of $$\dot{x}=A\, x, \; x(t_0)=x_0$$ x ˙ = A x , x ( t 0 ) = x 0 . Appl. Math. Sci. 2(20), 961–974 (2008)

4. Kohaupt, L.: Solution of the matrix eigenvalue problem $$V A + A^{\ast } V = \mu V$$ V A + A * V = μ V with applications to the study of free linear systems. J. Comput. Appl. Math. 213(1), 142–165 (2008)

5. Kohaupt, L.: Solution of the vibration problem $$M\ddot{y}+B\dot{y}+K y = 0, \, y(t_0)=y_0, \, \dot{y}(t_0)=\dot{y}_0$$ M y ¨ + B y ˙ + K y = 0 , y ( t 0 ) = y 0 , y ˙ ( t 0 ) = y ˙ 0 without the hypothesis $$B M^{-1} K = K M^{-1} B$$ B M - 1 K = K M - 1 B or $$B = \alpha M + \beta K$$ B = α M + β K . Appl. Math. Sci. 2(41), 1989–2024 (2008)

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