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We discuss the convergence of sequence of subspaces of an inner product space. This paper is an extension of the work by Manuharawti et al [1 and 2]. In this paper, we present a concept of convergence of sequence of n-dimentional subspaces of an inner product space. The properties of the concept are established. Moreover, we also study  its connection with angles in an inner product space.

We have a method to obtain the result in this research. The first study, we study about Grassmannian space and show the space is an metric space. After that, we will define convergen sequence in The Grassmannian space. To obtain the result, we use some basic properties of norm for showing the connection between angles in an inner product space.

 

Reference

[1]         Manuharawati, D.W. Yunianti, M. Jakfar, “A Sequence Convergence of Dimensional Subspace in a Normed Spaceâ€, Journal of Physics: Conf. Series, vol. 1108, Article ID 012085, 2018.

Manuharawati, D.W. Yunianti, M. Jakfar, “The Concept of Convergence for 2-Dimensional Subspaces Sequence in Normed Spacesâ€, submitted.

Convergence of sequence; inner product spaces; Grassmannian spaces.