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Consider two subspaces of a Hadamard matrix, whose columns are orthogonal. H = hadamard(8); A = H(:,2:4); B = H(:,5:8); Note that matrices A and B are different sizes - A has three columns and B four. It is not necessary that two subspaces be the same size in order to find the angle between them. Geometrically, this is the angle between two hyperplanes embedded in a higher dimensional space.

Consider two subspaces of a Hadamard matrix, whose columns are orthogonal. H = hadamard(8); A = H(:,2:4); B = H(:,5:8); Note that matrices A and B are different sizes - A has three columns and B four. It is not necessary that two subspaces be the same size in order to find the angle between them. Geometrically, this is the angle between two hyperplanes embedded in a higher dimensional space.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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Consider two subspaces of a Hadamard matrix, whose columns are orthogonal. H = hadamard(8); A = H(:,2:4); B = H(:,5:8); Note that matrices A and B are different sizes - A has three columns and B four. It is not necessary that two subspaces be the same size in order to find the angle between them. Geometrically, this is the angle between two hyperplanes embedded in a higher dimensional space.
Transcribed Image Text:Consider two subspaces of a Hadamard matrix, whose columns are orthogonal. H = hadamard(8); A = H(:,2:4); B = H(:,5:8); Note that matrices A and B are different sizes - A has three columns and B four. It is not necessary that two subspaces be the same size in order to find the angle between them. Geometrically, this is the angle between two hyperplanes embedded in a higher dimensional space.
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