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n-Inner Products, n-Norms, and Angles Between Two Subspaces
a Department of Mathematics, Bandung Institute of Technology, Bandung, 40132, Indonesia
[vc_row][vc_column][vc_row_inner][vc_column_inner][vc_separator css=”.vc_custom_1624529070653{padding-top: 30px !important;padding-bottom: 30px !important;}”][/vc_column_inner][/vc_row_inner][vc_row_inner layout=”boxed”][vc_column_inner width=”3/4″ css=”.vc_custom_1624695412187{border-right-width: 1px !important;border-right-color: #dddddd !important;border-right-style: solid !important;border-radius: 1px !important;}”][vc_empty_space][megatron_heading title=”Abstract” size=”size-sm” text_align=”text-left”][vc_column_text]© 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].[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Author keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Angles between subspaces,Cauchy-Schwarz inequality,Cosine of the angles,Dimensional subspace,Inner product,Inner product space,N-normed spaces,Orthogonality[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Indexed keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Angles between subspaces,Inner product spaces,n-inner pruduct spaces,n-normed spaces[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Funding details” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”DOI” size=”size-sm” text_align=”text-left”][vc_column_text]https://doi.org/10.1002/9781119414421.ch13[/vc_column_text][/vc_column_inner][vc_column_inner width=”1/4″][vc_column_text]Widget Plumx[/vc_column_text][/vc_column_inner][/vc_row_inner][/vc_column][/vc_row][vc_row][vc_column][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][/vc_column][/vc_row]