Orthogonality Test
Orthogonality Test - Related Videos
01:26
Orthogonal Trajectories
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2026
Orthogonal trajectories describe the geometric relationship between two families of curves that intersect each other at right angles. One illustrative case involves a family of parabolas that open sideways along the x-axis. These curves share a common shape but differ by a scaling parameter, resulting in a set of curves that all pass through the origin and widen at different rates.Determining Orthogonal TrajectoriesTo identify the orthogonal trajectories for these parabolas, the first step...
10:32
Orthogonal Protein Purification Facilitated by a Small Bispecific Affinity Tag
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Cited by 7 •
2012
A novel and highly efficient two-step affinity chromatography protocol has been developed and is described in detail. The method is based on a small purification tag with two inherent affinities and is applicable to a wide range of target proteins with different properties.
08:43
Calibration Procedures for Orthogonal Superposition Rheology
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Cited by 4 •
2020
We present a detailed calibration protocol for a commercial orthogonal superposition rheology technique using Newtonian fluids including end-effect correction factor determination methods and recommendations for best practices to reduce experimental error.
12:57
Resonance Fluorescence of an InGaAs Quantum Dot in a Planar Cavity Using Orthogonal Excitation and Detection
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Cited by 5 •
2017
Resonant excitation of a single self-assembled quantum dot can be achieved using an excitation mode orthogonal to the fluorescence collection mode. We demonstrate a method using the waveguide and Fabry-Perot modes of a planar microcavity surrounding the quantum dots. The method allows complete freedom in the detection polarization.
08:46
Using Synchrotron Radiation Microtomography to Investigate Multi-scale Three-dimensional Microelectronic Packages
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Cited by 5 •
2016
For this study synchrotron radiation micro-tomography, a non-destructive three-dimensional imaging technique, is employed to investigate an entire microelectronic package with a cross-sectional area of 16 x 16 mm. Due to the synchrotron's high flux and brightness the sample was imaged in just 3 min with an 8.7 µm spatial resolution.
FAQs
The inner product determines how agreement between two functions or signals is measured. In this test, it can include an integral of their product over a specified interval, together with a weighting rule or boundary conditions. Changing those conditions changes the criterion, so engineers must state the inner product before interpreting a zero result or comparing components.
Boundary and weighting conditions establish the mathematical context in which two functions are compared. The same pair may produce different inner-product values when the interval, weighting rule, or boundary requirements change. Specifying these conditions prevents ambiguous conclusions and ensures that an orthogonality result matches the physical or analytical model being studied.
The calculation follows the chosen representation. For finite-dimensional vectors, engineers evaluate a dot product directly. For functions or signals, they commonly integrate the product over a defined interval and may include weighting or boundary conditions. Thus, the underlying criterion remains an inner-product comparison, while the mathematical operation reflects the type of data.
First, identify the two vectors, functions, or signals and select the appropriate inner product. Next, specify the interval, weighting conditions, or boundary conditions when the objects are functions or signals. Evaluate the dot product or integral, then interpret the result within that defined framework. This workflow supports consistent construction of bases and separation of components.
The test is useful when engineers need to construct coordinate bases, separate signal components, analyze vibration modes, or simplify coupled equations. These applications occur across modeling, communications, control systems, and structural design. By identifying components that satisfy the selected orthogonality criterion, engineers can organize calculations around relationships that make the resulting analysis more manageable.
In vibration analysis, engineers can examine whether mode-related functions satisfy the required orthogonality conditions under a defined inner product. This helps distinguish vibration modes and contributes to simplified mathematical descriptions of structural behavior. In structural design, the same criterion supports organized modeling by providing a way to assess relationships among functions used to represent the system.