Generalized Inversions of Hadamard and Tensor Products for Matrices

Saburou Saitoh^{*}

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References

[1] Asaduzzaman, M. and Saitoh, S. (2003) Inverses of a Family of Matrices and Generalizations of Pythagorean Theorem. Panamerican Mathematical Journal, 13, 45-53.

[2] Mai, W., Yan, M., Qian, T., Riva, M.D. and Saitoh, S. (1013) A Matrix Inequality for the Inversions of the Restrictions of a Positive Definite Hermitian Matrix. Advances in Linear Algebra & Matrix Theory, 3, 55-58.

[3] Mond, B., Pecaric, J.E. and Saitoh, S. (1994) History, Variations and Generalizations of an Inequality of Marcus. Riazi: Journal of Karachi Mathematical Association, 16, 7-15.

[4] Saitoh, S. (1982) Positive Definite Hermitian Matrices and Reproducing Kernels. Linear Algebra and Its Applications, 48, 119-130.

http://dx.doi.org/10.1016/0024-3795(82)90102-1

[5] Saitoh, S. (1987) Quadratic Inequalities Deduced From the Theory of Reproducing Kernels. Linear Algebra and Its Applications, 93, 171-178. http://dx.doi.org/10.1016/S0024-3795(87)90322-3

[6] Saitoh, S. (1988) Quadratic Inequalities Associated with Integrals of Reproducing Kernels. Linear Algebra and Its Applications, 101, 269-280.

http://dx.doi.org/10.1016/0024-3795(88)90154-1

[7] Saitoh, S. (2003) Generalizations of the Triangle Inequality. Journal of Inequalities in Pure and Applied Mathematics, 4, Article 62.

[8] Sawano, Y. (2011) Pasting Reproducing Kernel Hilbert Spaces. Jaen Journal on Approximation, 3, 135-141.

[9] Yamada, A. (2012) Oppenheim’s Inequality and RKHS. Mathematical Inequalities and Applications, 15, 449-456.

[10] Saitoh, S. (1997) Integral Transforms, Reproducing Kernels and their Applications. Pitman Research Notes in Math. Series 369, Addison Wesley Longman, Harlow.

[11] Saitoh, S. (2010) Theory of Reproducing Kernels: Applications to Approximate Solutions of Bounded Linear Operator Functions on Hilbert Spaces. American Mathematical Society Translations: Series 2, 230, Amer. Math. Soc., Providence, RI.

[12] Castro, L.P., Fujiwara, H., Saitoh, S., Sawano, Y., Yamada, A. and Yamada, M. (2012) Fundamental Error Estimates Inequalities for the Tikhonov Regularization Using Rreproducing Kernels. International Series of Numerical Mathematics 161, Inequalities and Appications 2010, Springer, Basel, 87-101.

[13] Castro, L.P., Saitoh, S., Sawano, Y. and Silva, A.S. (2012) Discrete Linear Differential Equations. Analysis, 32, 181- 191.

http://dx.doi.org/10.1524/anly.2012.1104

[14] Castro, L.P., Fujiwara, H., Rodrigues, M. M., Saitoh, S. and Tuan, V.K. (2014) Aveiro Discretization Method in Mathematics: A New Discretization Principle. In: Pardalos, P. and Rassias, T.M., Eds., Mathematics without Boundaries: Surveys in Pure Mathematics, in press.

[15] Castro, L.P., Fujiwara, H., Qian, T. and Saitoh, S. (2014) How to Catch Smoothing Properties and Analyticity of Functions by Computers? In: Pardalos, P. and Rassias, T.M., Eds., Mathematics without Boundaries: Surveys in Interdisipinary Research, in press.

[16] Castro, L. P., Saitoh, S. and Yamada, A. (2014) Representations of Solutions of Tichhonov Functional Equations and Applications to Multiplication Operators of the Szego Spaces (submitted).

[17] Takahashi, S. (2014) On the Identities 100/0=0 and 0/0=0. (submitted).

[18] Kuroda, T., Michiwaki, H., Saitoh, S. and Yamane, M. (2014) New Meanings of the Division by Zero and Interpretations on 100/0 = 0 and on 0/0 = 0. International Journal of Applied Mathematics, 27, 191-198.