Throught a generalized inverse

• Autorzy: Stępniak C.
• Języki publikacji: EN

Abstrakty

EN

Traditionally, the existence of a generalized inverse of a matrix A is derived in an indirect way from the matrix equation AXA = A. We reach this result in a direct and constructive manner, based on spectral decomposition. Moreover, some new results on its characterization and on representation of the entire set of generalized inverses are given. Usefulness of these results is demonstrated in examples.

Słowa kluczowe

EN

generalized inverse; Moore-Penrose inverse; linear algebra

PL

odwrotność uogólniona; odwrotność Moore-Penrose; algebra liniowa

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2008
• Tom: Vol. 41, nr 2
• Strony: 291--296
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Stępniak C.

• Institute of Mathematics University of Rzeszów, Rejtana 16 A 35-959 Rzeszów, Poland

Bibliografia

• [1] R. B. Bapat, (2000). Linear Algebra and Linear Models, 2nd Edn., Springer-Verlag, New York.
• [2] A. Ben-Israel and T. N. E. Greville (2003). Generalized Inverses. Theory and Applications, 2nd Edn, Springer-Verlag, New York.
• [3] S. L. Campbell and C. D. Meyer, Jr (1991). Generalized Inverses of Linear Transformations, Corrected reprint of the 1979 original, Dover Publications, Inc., New York.
• [4J R. M. Pringle and A. A. Rayner (1971). Generalized Inverse of Matrices with Applications to Statistics, Griffin, London.
• [5] C. R. Rao (1955), Analysis of dispersion for multiply classified data with unequal numbers in cells, Sankhyā 15, 253-280.
• [6] C. R. Rao and S. K. Mitra (1971). Generalized Inverse of Matrices and its Applications, Wiley, New York.