© 2018 John Wiley & Sons, Inc. All rights reserved.In this note we discuss the concepts of n-inner products and n -norms for any n ∈ N, which are generalizations of the concepts of inner products and norms. The definition of n -inner products was originally formulated by Misiak [36], while the notion of n -norms was developed by Gähler [2-4]. We discuss some results on n -inner product spaces and n -normed spaces, including the topology and the notion of orthogonality in n -normed spaces. Related to the n -inner product (and its deduced n -norm), we have the Cauchy-Schwarz inequality and accordingly the cosine of the angle between two n -dimensional subspaces intersecting on an (n – 1) -dimensional subspace. We are then interested in the formula for the angle between two subspaces (which may be of different dimensions) of an inner product space in general. This note summarizes the results in [5-7].

Angles between subspaces,Cauchy-Schwarz inequality,Cosine of the angles,Dimensional subspace,Inner product,Inner product space,N-normed spaces,Orthogonality

Angles between subspaces,Inner product spaces,n-inner pruduct spaces,n-normed spaces

https://doi.org/10.1002/9781119414421.ch13