Topic
Orthogonality
About: Orthogonality is a research topic. Over the lifetime, 3723 publications have been published within this topic receiving 59256 citations. The topic is also known as: orthogonal.
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01 Jan 2013
TL;DR: In this paper, a multidimensional generalization of this theorem relates to an interaction of skew symmetry and orthogonality features, i.e., properties of determinants and other multilinear functions, and Euclidean spaces.
Abstract: Readers likely recall the following elementary geometric statement: if the sides of an angle α in a Euclidean plane are orthogonal to the sides of an angle β, then α=β or α+β=180°; in other words, |cos α|=|cos β|. A multidimensional generalization of this theorem relates to an interaction of skew symmetry and orthogonality features, i.e., properties of determinants and other multilinear functions, and Euclidean spaces; we presume readers are familiar with these features within the scope of a common university course, and on this basis we develop the tools necessary to prove this generalization. These tools have multiple applications. For examples, they allow us to extend a definition of the angle between straight lines or between hyperplanes to k-dimensional planes of ℝ n for every 0
18 Jun 2011
TL;DR: In this paper, the concept of orthogonal non-tensor bivariate wavelet packs is proposed by virtue of analogy method and iteration method and their orthogonality property is investigated by using time-frequency analysis method and variable se-paration approach.
Abstract: In this paper, the concept of orthogonal non-tensor bivariate wavelet packs, which is the generalization of orthogonal univariate wavelet packs, is pro -posed by virtue of analogy method and iteration method. Their orthogonality property is investigated by using time-frequency analysis method and variable se-paration approach. Three orthogonality formulas concerning these wavelet packs are obtained. Moreover, it is shown how to draw new orthonormal bases of space L 2(R 4) from these wavelet wraps. A procedure for designing a class of orthogonal vector-valued finitely supported wavelet functions is proposed by virtue of filter bank theory and matrix theory.
TL;DR: In this paper , a method of tripling for a three-level design is proposed for constructing a design that can accommodate a large number of factors by combining all possible level permutations of its initial design.
Abstract: A method of tripling for a three-level design, which triples both the run size and the number of factors of the initial design, has been proposed for constructing a design that can accommodate a large number of factors by combining all possible level permutations of its initial design. Based on the link between the indicator functions of a triple design and its initial design, the close relationships between a triple design and its initial design are built from properties such as resolution and orthogonality. These theoretical results present a closer look at a triple design and provide a solid foundation for a design constructed using the tripling method, where the constructed designs have better properties, such as high resolution and orthogonality, and are recommended for application in high dimension topics of statistics or large-scale experiments.