Abstract
The subject of this chapter is the homogeneous linear system
where w(z) = (w1(z),... wn(z))T is a complex-valued vector function and A(z)=(aij (z)) is a complex-valued n x n matrix. We also investigate homogeneous linear differential equations of higher order. Let G C C be open and denote by H(G) the complex linear space of functions that are single-valued and holomorphic on \( w(z) \in H(G)orA(z) \in H(G) \) if every component Wi (z) or aij (z) belongs to H(G). Compatible norms for complex column vectors and n x n matrices will be denoted by single vertical bars, and the properties (14.2-3),
are taken for granted. Throughout this chapter, matrices are understood to be complex n x n matrices.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media New York
About this chapter
Cite this chapter
Walter, W. (1998). Complex Linear Systems. In: Ordinary Differential Equations. Graduate Texts in Mathematics, vol 182. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0601-9_6
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0601-9_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6834-5
Online ISBN: 978-1-4612-0601-9
eBook Packages: Springer Book Archive