Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-06-08T23:09:40.845Z Has data issue: false hasContentIssue false
  • English
  • Français

The Frechet Differential of a Primary Matrix Function

Published online by Cambridge University Press:  20 November 2018

David L. Powers
David L. Powers*
Affiliation:
Clarkson College of Technology, Potsdam, New York
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let X be a given complex matrix of order n. If f(z) is analytic at the eigenvalues of X, one may define the primary matrix function f(X) with stem function f(z) by using any of several well-known methods: for instance, canonical forms, power series, or interpolating polynomials [9].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 3 , June 1973 , pp. 554 - 559
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Diendonné, J., Foundations of modern analysis (Academic Press, New York, 1960).Google Scholar
2. Fer, F., Résolution de Véquation matricielle dV/dt = pV par produit infini d'exponentielles matricielles, Bull, de l'Acad. R. de Belg., Classe des Sciences U (1958), 818-829.Google Scholar
3. Jacobson, N., Abstract derivation and Lie algebras, Trans. Amer. Math. Soc. 42 (1937), 206–224.Google Scholar
4. Neudecker, H., A note on Kronecker matrix products and matrix equation systems, SI AM J. Appl. Math. 17 (1969), 603–606.Google Scholar
5. Penrose, R., On best approximate solutions of linear matrix equations, Proc. Cambridge Philos. Soc. 52 (1956), 17–19.Google Scholar
6. Phillips, H. B., Functions of matrices, Amer. J. Math. U (1919), 266-278.Google Scholar
7. Powers, D. L., On the differentials of certain matrix functions, Can. J. Math. 23 (1971), 282–286.Google Scholar
8. Rinehart, R. F., The derivative of a matric function, Proc. Amer. Math. Soc. 7 (1955), 2–5.Google Scholar
9. Rinehart, R. F., The equivalence of definitions of a matric function, Amer. Math. Monthly 62 (1955), 395–414.Google Scholar
10. Rinehart, R. F., Extension of the derivative concept for functions of matrices, Proc. Amer. Math. Soc. 8 (1957), 329–335.Google Scholar
11. Rinehart, R. F., The differential of a primary matrix function, Rend. Circ. Mat. Palermo 15 (1966), 209–215.Google Scholar
12. Roth, W. E., On k-commutative matrices, Trans. Amer. Math. Soc. 39 (1936), 483–495.Google Scholar
13. Szeri, A. Z. and Powers, D. L., Pivoted plane pad bearings: a variational solution. Trans. ASME(F) 3 (1970), 466–471.Google Scholar