Abstract
It will be convenient to use vector notation even though we are not concerned with vectors in the sense of entities which are invariant under coordinate transformations. We shall therefore use the word “vector” simply to mean a matrix of one row and n columns (or n rows and one column as the case may be). The components of a vector are to be thought of as representing a table of a continuous function. Instead of the number of nodes of an eigenfunction, we consider the number of variations of sign in the sequence of components of an eigenvector.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
All vectors in the same octant of 3-dimensional space have the same sign sequence. With each octant, therefore, there is associated a variation number. A border vector is a vector which lies in a coordinate plane separating two octants with different variation numbers. A border vector always has the variation number of that neigboring octant whose variation number is lowest.
Rights and permissions
Copyright information
© 1954 Springer Basel AG
About this chapter
Cite this chapter
Sinden, F.W. (1954). Interior and Border Vectors. In: An Oscillation Theorem for Algebraic Eigenvalue Problems and its Applications. Mitteilungen aus dem Institut für angewandte Mathematik, vol 4. Springer, Basel. https://doi.org/10.1007/978-3-0348-4149-8_2
Download citation
DOI: https://doi.org/10.1007/978-3-0348-4149-8_2
Publisher Name: Springer, Basel
Print ISBN: 978-3-0348-4075-0
Online ISBN: 978-3-0348-4149-8
eBook Packages: Springer Book Archive