Orthogonal Transformation definition of Orthogonal Transformation in the Free Online Encyclopedia.

orthogonal transformation [ȯr′thäg·ən·əl ‚tranz‚fər′mā·shən]

(mathematics)

A linear transformation between real inner product spaces which preserves the length of vectors.

Orthogonal Transformation

a linear transformation of a Euclidean vector space that preserves the lengths or (equivalently) the scalar products of vectors. In an orthonormal basis an orthogonal transformation corresponds to an orthogonal matrix. Orthogonal transformations form a group, the group of rotations of the given Euclidean space about the origin. In three-dimensional space an orthogonal transformation reduces to a rotation through a certain angle about some axis passing through the origin O, if the determinant of the corresponding orthogonal matrix is +1. If the determinant is —1, then the rotation must be supplemented by a reflection in the plane passing through O perpendicular to the axis of rotation. In two-dimensional space, that is, in a plane, an orthogonal transformation defines a rotation through a certain angle about O or a reflection relative to some line passing through O. Orthogonal transformations are used to reduce a quadratic form to the principal axes.

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No references found			For an orthogonal transformation M, this requires that [psi] = [[psi]. Modeling the development of elastic anisotropy as a result of plastic ... by Goel, A.; Strabala, K.; Negahban, M.; Turner, J.A. / Polymer Engineering and Science 19 Orthogonal Transformations and Their Invariants. Reissue of Classic Publication Provides an Overview of ... by Business Wire			Orthognathism Orthognathous Occlusion Orthogneiss orthogonal orthogonal antennas orthogonal basis orthogonal complement orthogonal crystal orthogonal family orthogonal functions orthogonal group orthogonal instruction set orthogonal Latin squares orthogonal lines Orthogonal Matrix orthogonal parity check Orthogonal Polynomial orthogonal polynomials Orthogonal Projection orthogonal series orthogonal spaces orthogonal sum orthogonal system Orthogonal System of Functions orthogonal trajectory Orthogonal Transformation orthogonal vectors Orthogonality orthogonalization orthogonalized plane-wave method Orthogram orthographic chart Orthographic Projection Orthography orthohelium orthohexagonal axes orthohydrogen orthohydrous coal orthokeratology orthokinesis ortholignitous coal orthologous locus orthomagmatic stage orthometric correction orthometric height orthomimic feldspars orthomorphic orthomorphic chart orthomorphic map projection Orthomyxoviridae Orthonectida			Orthogonal polynomials Orthogonal Polynomials and Special Functions Orthogonal Polynomials and Special Functions Network Orthogonal Polynomials on the Unit Circle Orthogonal Polynomials, Special Functions and Applications orthogonal projection orthogonal projection Orthogonal Projection Approximation Subspace Tracking Orthogonal Projection Routine Orthogonal Quadrature Phase-Shift Keying Orthogonal Rayleigh Quotient Iteration Method Orthogonal Region orthogonal series Orthogonal Short-Time Fourier Orthogonal Space-Time Orthogonal Space-Time Block Code Orthogonal Space-Time Coding for Continuous-Phase Modulation orthogonal spaces Orthogonal subspace Orthogonal subspace Orthogonal subspaces Orthogonal subspaces orthogonal sum Orthogonal system Orthogonal System of Functions Orthogonal Tetrahedral Quotient Orthogonal trajectory Orthogonal Transformation Orthogonal Transmit Diversity Orthogonal Transmit Diversity-Simulcast Orthogonal Transmit Spatial Multiplexing Orthogonal variable spreading factor Orthogonal vector Orthogonal vector Orthogonal vectors Orthogonal vectors Orthogonal Wavelet Packet Orthogonal Wavelet Transform Orthogonal-Field-Alternation Gel Electrophoresis Orthogonal-Plane Fluorescence Optical Sectioning Orthogonal-Transfer Charge-Coupled Device Orthogonal-Waveform Multiple Access Orthogonalisation orthogonality orthogonality Orthogonality Constrained Basis Set Expansion Procedure Orthogonality Restoring Combining Orthogonalization Orthogonalized Atomic Orbital Orthogonalized Hybrid Atomic Orbital Orthogonalized Linear Combination of Atomic Orbitals Orthogonalized Modulated Plane Wave Orthogonalized Plane Wave orthogonalized plane-wave method Orthogonalized Stochastic Approximation