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Type of mathematical array
In mathematics, an orthogonal array (more specifically, a fixed-level orthogonal array) is a table ("array") whose entries come from a fixed finite set
Orthogonal_array
Software testing technique
Orthogonal array testing is a systematic and statistically-driven black-box testing technique employed in the field of software testing. This method is
Orthogonal_array_testing
Mathematical problem
combinatorics, two Latin squares of the same size (order) are said to be orthogonal if when superimposed the ordered paired entries in the positions are all
Mutually orthogonal Latin squares
Mutually_orthogonal_Latin_squares
Square array with symbols that each occur once per row and column
obtain a set of n2 triples called the orthogonal array representation of the square. For example, the orthogonal array representation of the Latin square
Latin_square
Generalization of perpendicularity
space is called pairwise orthogonal if each pairing of them is orthogonal. Such a set is called an orthogonal set (or orthogonal system). If the vectors
Orthogonality_(mathematics)
Topics referred to by the same term
Standard array in coding theory Matrices, a rectangular array of numbers in rows and columns Costas array Monge array Holors Orthogonal array Intersection
Array
Statistical sampling technique
(1992). "Orthogonal arrays for computer experiments, integration and visualization". Statistica Sinica. 2: 439–452. Ye, K.Q. (1998). "Orthogonal column
Latin_hypercube_sampling
Radar with multiple antennas for transmitting and receiving
phased array system, additional antennas and related hardware are needed to improve spatial resolution. MIMO radar systems transmit mutually orthogonal signals
MIMO_radar
Checking software against expectations
requirements Manual testing – Testing software without automation Orthogonal array testing – Software testing technique Pair testing – Software testing
Software_testing
Software testing
include exception handling, regression testing, functional testing, and orthogonal array testing. Gray-box testing is particularly used for testing web applications
Gray-box_testing
the saturated array allows three factors to be tested in four tests rather than in eight, as would be required by a standard orthogonal array. v t e
Saturated_array
Computer programming methodology
In computer programming, orthogonality means that operations change just one thing without affecting others. The term is most-frequently used regarding
Orthogonality_(programming)
Statistical approach
estimated independently without (or with minimal) confounding. Also orthogonality provides minimum variance estimates of the model coefficient so that
Response_surface_methodology
Statistical methods to improve the quality of manufactured goods
proposed extending each experiment with an "outer array" (possibly an orthogonal array); the "outer array" should simulate the random environment in which
Taguchi_methods
Method of encoding digital data on multiple carrier frequencies
In telecommunications, orthogonal frequency-division multiplexing (OFDM) is a type of digital transmission used in digital modulation for encoding digital
Orthogonal frequency-division multiplexing
Orthogonal_frequency-division_multiplexing
Array of numbers
In mathematics, a matrix (pl.: matrices) is a rectangular array of numbers or other mathematical objects with elements or entries arranged in rows and
Matrix_(mathematics)
Design of tasks
in 1946. About the same time, C. R. Rao introduced the concepts of orthogonal arrays as experimental designs. This concept played a central role in the
Design_of_experiments
Software testing method
generated by Microsoft's "pict" tool, are shown below. Software testing Orthogonal array testing Berger, Bernie (2003). "Efficient Testing with All-Pairs" (PDF)
All-pairs_testing
Generalized randomized block design (GRBD) Latin square Graeco-Latin square Orthogonal array Latin hypercube Repeated measures design Crossover study Randomized
Generalized randomized block design
Generalized_randomized_block_design
Generalized randomized block design (GRBD) Latin square Graeco-Latin square Orthogonal array Latin hypercube Repeated measures design Crossover study Randomized
Fisher's_inequality
Indian-American mathematician (1920–2023)
other contributions include the Fisher–Rao theorem, Rao distance, and orthogonal arrays. He was the author of 15 books and authored over 400 journal publications
C._R._Rao
Bias in causal inference
Generalized randomized block design (GRBD) Latin square Graeco-Latin square Orthogonal array Latin hypercube Repeated measures design Crossover study Randomized
Confounding
Statistical theorem in the analysis of variance
{\displaystyle \sum _{i}r_{i}=\operatorname {rank} (A)} . But after an orthogonal transform, A = diag ( I M , 0 ) {\displaystyle A=\operatorname {diag}
Cochran's_theorem
Two-dimensional cellular automaton
grid. The universe of the Game of Life is an infinite, two-dimensional orthogonal grid of square cells, each of which is in one of two possible states,
Conway's_Game_of_Life
classes. An alternate representation of a Latin square is given by an orthogonal array. For a Latin square of order n this is an n2 × 3 matrix with columns
Small Latin squares and quasigroups
Small_Latin_squares_and_quasigroups
Set of multiple antennas which work together
the Yagi antenna. Let us consider a linear array whose elements are arranged along the x-axis of an orthogonal Cartesian reference system. It is assumed
Antenna_array
Statistical phenomenon where some effects appear the same
mixed-level array. In this section fractional designs are allowed to be mixed-level unless explicitly restricted. A key parameter of an orthogonal array is its
Aliasing (factorial experiments)
Aliasing_(factorial_experiments)
Any of a set of standard configurations of Redundant Arrays of Independent Disks
RAID levels comprise a basic set of RAID ("redundant array of independent disks" or "redundant array of inexpensive disks") configurations that employ the
Standard_RAID_levels
Japanese statistician
Shewhart. While working at the SQC Unit of ISI, he was introduced to the orthogonal arrays invented by C. R. Rao - a topic which was to be instrumental in enabling
Genichi_Taguchi
Polynomial sequence
mathematics, the Zernike polynomials are a sequence of polynomials that are orthogonal on the unit disk. Named after optical physicist Frits Zernike, laureate
Zernike_polynomials
Method for dividing a secret among multiple parties
Homomorphic secret sharing – A simplistic decentralized voting protocol. Orthogonal array – Used to construct some threshold schemes. Publicly verifiable secret
Secret_sharing
Collection of statistical models
complex designs the lack of balance leads to further complications. "The orthogonality property of main effects and interactions present in balanced data does
Analysis_of_variance
Experimental design in statistics
and SPIRIT extensions. Combinatorial design Design of experiments Orthogonal array Plackett–Burman design Taguchi methods Welch's t-test This choice gives
Factorial_experiment
Orthonormalization of a set of vectors
S=\{\mathbf {v} _{1},\ldots ,\mathbf {v} _{k}\}} for k ≤ n and generates an orthogonal set S ′ = { u 1 , … , u k } {\displaystyle S'=\{\mathbf {u} _{1},\ldots
Gram–Schmidt_process
Design of experiments to collect similar contexts together
Generalized randomized block design (GRBD) Latin square Graeco-Latin square Orthogonal array Latin hypercube Repeated measures design Crossover study Randomized
Blocking_(statistics)
Property of term rewriting systems
{\displaystyle {\begin{array}{lrcl}\rho _{1}:\ &f(x,y)&\rightarrow &g(y)\\\rho _{2}:\ &h(y)&\rightarrow &f(g(y),y)\end{array}}} is orthogonal—it is easy to observe
Orthogonality (term rewriting)
Orthogonality_(term_rewriting)
Coordinate system using perpendicular axes
origin and has (0, 0) as coordinates. The axes directions represent an orthogonal basis. The combination of origin and basis forms a coordinate frame called
Cartesian_coordinate_system
Experimental design that is optimal with respect to some statistical criterion
S-optimality This criterion maximizes a quantity measuring the mutual column orthogonality of X and the determinant of the information matrix. T-optimality This
Optimal_experimental_design
American statistician
On Orthogonal Arrays of Strength Four and Their Applications. She later published this work, "the first significant progress on orthogonal arrays of strength
Rita_Zemach
British-American mathematician (born 1939)
1998. A. S. Hedayat, Neil James Alexander Sloane and J. Stufken, Orthogonal Arrays: Theory and Applications, Springer-Verlag, NY, 1999. G. Nebe, E. M
Neil_Sloane
Branch of mathematics
Two vectors are orthogonal if ⟨u, v⟩ = 0. An orthonormal basis is a basis where all basis vectors have length 1 and are orthogonal to each other. Given
Linear_algebra
Classification of orthogonal polynomials
way of organizing orthogonal polynomials of hypergeometric or basic hypergeometric type into a hierarchy. For the classical orthogonal polynomials discussed
Askey_scheme
General linear model that blends ANOVA and regression
Generalized randomized block design (GRBD) Latin square Graeco-Latin square Orthogonal array Latin hypercube Repeated measures design Crossover study Randomized
Analysis_of_covariance
Family of orthogonal polynomials
mathematics, Hahn polynomials are a family of orthogonal polynomials in the Askey scheme of hypergeometric orthogonal polynomials, introduced by Pafnuty Chebyshev
Hahn_polynomials
q_{k}(i)} , play a prominent role in the theory. They satisfy well-defined orthogonality relations. The p-numbers are the eigenvalues of the adjacency matrix
Bose–Mesner_algebra
Experimental design framework
Generalized randomized block design (GRBD) Latin square Graeco-Latin square Orthogonal array Latin hypercube Repeated measures design Crossover study Randomized
Bayesian_experimental_design
concept of rank is used to treat an orthogonal array in terms of its subarrays. For example, a two-dimensional array may be dealt with at rank 2 as the
Rank_(J_programming_language)
Ordination (statistics) Ornstein–Uhlenbeck process Orthogonal array testing Orthogonality Orthogonality principle Outlier Outliers ratio Outline of probability
List_of_statistics_articles
the Gaussian matrix ensembles. The three main examples are the circular orthogonal ensemble (COE) on symmetric unitary matrices, the circular unitary ensemble
Circular_ensemble
Generalized randomized block design (GRBD) Latin square Graeco-Latin square Orthogonal array Latin hypercube Repeated measures design Crossover study Randomized
Scheirer–Ray–Hare_test
Symmetric arrangement of finite sets
Mendelsohn triple system MTS(|Q|,1). This construction is reversible. Orthogonal arrays Packing designs A quasi-3 design is a symmetric design (SBIBD) in
Combinatorial_design
Measure of how much of an antenna's signal is transmitted in one direction
of array elements. For a planar array, the computation of directivity is more complicated and requires consideration of the positions of each array element
Directivity
Vectors mapped to 0 by a linear map
kernel of A, if and only if x is orthogonal (or perpendicular) to each of the row vectors of A (since orthogonality is defined as having a dot product
Kernel_(linear_algebra)
Theory in statistics
satisfies certain polynomial properties; this leads one into the realm of orthogonal polynomials. In particular, some universal bounds are derived for codes
Association_scheme
Russian mathematician (1935–2017)
Mainz, Germany, September 22–25, 1996, 657–661. VI Levenshtein, Split orthogonal arrays and maximum independent resilient systems of functions, Designs, Codes
Vladimir_Levenshtein
User interface element
the kebab button characters in a row, such as ⁝⁝⁝ U+25A6 ▦ SQUARE WITH ORTHOGONAL CROSSHATCH FILL U+130D1 𓃑 EGYPTIAN HIEROGLYPH D067H It has been argued
Hamburger_button
British statistician and geneticist (1919–2000)
Generalized randomized block design (GRBD) Latin square Graeco-Latin square Orthogonal array Latin hypercube Repeated measures design Crossover study Randomized
Oscar_Kempthorne
Test a component of a marketing campaign
nine combinations to test. Taguchi methods (namely Taguchi Taguchi orthogonal arrays) can be used in the design of experiments in order to reduce the variations
Multivariate testing in marketing
Multivariate_testing_in_marketing
Matrices similar to diagonal matrices
spaces. Additional geometric visualizations of orthogonal diagonalization, including reflection and orthogonal projection matrices, are available at Wikimedia
Diagonalizable_matrix
French mathematician (1843–1913)
Generalized randomized block design (GRBD) Latin square Graeco-Latin square Orthogonal array Latin hypercube Repeated measures design Crossover study Randomized
Gaston_Tarry
Method for analyzing revealed preferences
(2): 115–125. doi:10.1016/S0148-2963(99)00058-2. ISSN 0148-2963. "Orthogonal Arrays". support.sas.com. Retrieved 2015-11-04. "ChoiceMetrics | Ngene |
Choice_modelling
Experimental setup in behavioral sciences
Generalized randomized block design (GRBD) Latin square Graeco-Latin square Orthogonal array Latin hypercube Repeated measures design Crossover study Randomized
Paradigm_(experimental)
Generalized randomized block design (GRBD) Latin square Graeco-Latin square Orthogonal array Latin hypercube Repeated measures design Crossover study Randomized
Robust_parameter_design
Type of beamforming network
A Butler matrix is a beamforming network used to feed a phased array of antenna elements. Its purpose is to control the direction of a beam, or beams
Butler_matrix
Algebraic object with geometric applications
basis related to a particular coordinate system; those components form an array, which can be thought of as a high-dimensional matrix. Tensors have become
Tensor
In mathematics, the Meixner–Pollaczek polynomials are a family of orthogonal polynomials P(λ) n(x,φ) introduced by Meixner (1934), which up to elementary
Meixner–Pollaczek_polynomials
Relation of space and time in relativity theory
pair of conjugate hyperbolas, two conjugate diameters are hyperbolically orthogonal. This relationship of diameters was described by Apollonius of Perga and
Hyperbolic_orthogonality
Mathematical statistician (1908–2014)
concept of the complement of an oval, and her work with Rita Zemach on orthogonal arrays of strength four was described as "the first significant progress"
Esther_Seiden
Type of computer instruction set
engineering, an orthogonal instruction set is an instruction set architecture where all instruction types can use all addressing modes. It is "orthogonal" in the
Orthogonal_instruction_set
Branch of mathematical statistics
then with the introduction of association schemes by R. C. Bose. Orthogonal arrays were introduced by C. R. Rao also for experimental designs. The field
Algebraic_statistics
Global radio telescope array
The Event Horizon Telescope (EHT) is a telescope array consisting of a global network of radio telescopes. The EHT project combines data from several
Event_Horizon_Telescope
Isometry of the Euclidean plane
through the origin is obtained with all orthogonal matrices (i.e. with determinant 1 and −1) forming orthogonal group O(2). In the case of a determinant
Euclidean_plane_isometry
Generalized randomized block design (GRBD) Latin square Graeco-Latin square Orthogonal array Latin hypercube Repeated measures design Crossover study Randomized
W._H._Clatworthy
Astronomical observatory
camera. It will also permit employment of the new "Microcam", an orthogonal transfer array (OTA), with Pan-STARRS heritage. Other advanced camera systems
United States Naval Observatory Flagstaff Station
United_States_Naval_Observatory_Flagstaff_Station
Computer programming operation
computer programming, array slicing is an operation that extracts a subset of elements from an array and packages them as another array, possibly in a different
Array_slicing
Method of encoding digital data on multiple carrier frequencies
Non-orthogonal frequency-division multiplexing (N-OFDM) is a method of encoding digital data on multiple carrier frequencies with non-orthogonal intervals
Non-orthogonal frequency-division multiplexing
Non-orthogonal_frequency-division_multiplexing
Technical design of the components of a radar and its operation
frequency-orthogonal (slotted waveguide), spatially orthogonal (switched beamforming networks), or time-orthogonal beams. In case of time-orthogonal scanning
Radar_engineering
Functional programming language for arrays
1960s by Kenneth E. Iverson. Its central datatype is the multidimensional array. It uses a large range of special graphic symbols to represent most functions
APL_(programming_language)
A Riordan array is an infinite lower triangular matrix, D {\displaystyle D} , constructed from two formal power series, d ( t ) {\displaystyle d(t)} of
Riordan_array
Algebraic structure used in analysis
H=\left({\begin{array}{cc}1&0\\0&-1\end{array}}\right),\ E=\left({\begin{array}{cc}0&1\\0&0\end{array}}\right),\ F=\left({\begin{array}{cc}0&0\\1&0\end{array}}\right)
Lie_algebra
Device to reflect radiation back to its source
photographs and the retroreflectors have been used again. Lunokhod 2's array continues to return signals to Earth. Even under good viewing conditions
Retroreflector
Iterative method for approximating eigenvectors
&A^{n-1}b\end{bmatrix}}.} The columns of this matrix are not in general orthogonal, but we can extract an orthogonal basis, via a method such as Gram–Schmidt orthogonalization
Arnoldi_iteration
m/2 − 1 the Delsarte–Goethals code has strength 7 and is therefore an orthogonal array OA( 2 3 m − 1 , 2 m , Z 2 , 7 ) {\displaystyle 2^{3m-1},2^{m},\mathbb
Delsarte–Goethals_code
Research Institution in Kolkata, India
Cramér–Rao inequality and Rao-Blackwell Theorem, and introduction of orthogonal arrays in Design of Experiments. Anil Kumar Gain is known for his contributions
Indian_Statistical_Institute
Lobe in a discrete aperture antenna
is a plane wave incident orthogonal to the array (from boresight). For a uniformly weighted (un-tapered) uniform linear array, the steering vector is of
Grating_lobes
Classification of crystalline materials by their three-dimensional structural geometry
fixed point). A lattice system is a set of Bravais lattices (an infinite array of discrete points). Space groups (symmetry groups of a configuration in
Crystal_system
Four-dimensional number system
array}{rrrr}a&-b&-c&-d\\b&a&-d&c\\c&d&a&-b\\d&-c&b&a\end{array}}\right]&=a\left[{\begin{array}{rrrr}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{array
Quaternion
Concept in physics and mathematics
{\displaystyle (\mathbf {x} ,t)\mapsto (R\mathbf {x} ,t),} where R : R3 → R3 is an orthogonal transformation. As a Lie group, the group of Galilean transformations
Galilean_transformation
WiFi option
are orthogonal. This means that the STBC is designed such that the vectors representing any pair of columns taken from the coding matrix is orthogonal. The
Space–time_block_code
Least squares approximation of linear functions to data
least squares include inverting the matrix of the normal equations and orthogonal decomposition methods. Consider the linear equation where A ∈ R m × n
Linear_least_squares
Signal processing technique for sensor arrays
technique used in sensor arrays for directional signal transmission or reception. This is achieved by combining elements in an antenna array in such a way that
Beamforming
Engineering consultancy
Taguchi orthogonal arrays Plackett-Burman designs Latin hypercube designs Central composite designs D-optimal designs Taguchi robust design arrays User-defined
Red_Cedar_Technology
In mathematics, vector subspace
vector spaces, for example, orthogonal complements exist. However, these spaces may have null vectors that are orthogonal to themselves, and consequently
Linear_subspace
Group of rotations in 3 dimensions
Matrices for which this property holds are called orthogonal matrices. The group of all 3 × 3 orthogonal matrices is denoted O(3), and consists of all proper
3D_rotation_group
Kind of matrix
C_{2}=\left[{\begin{array}{rrr}1&0\\0&1\end{array}}\right]-{\frac {1}{2}}\left[{\begin{array}{rrr}1&1\\1&1\end{array}}\right]=\left[{\begin{array}{rrr}{\frac
Centering_matrix
Chinese mathematician and statistician (born 1940)
MR 2047311 Hedayat, A. S.; Sloane, N. J. A.; Stufken, J. (1999). Orthogonal arrays, theory and applications. New York: Springer. doi:10.1007/978-1-4612-1478-6
Fang_Kaitai
testing or methods which reduce the number of tested inputs, such as orthogonal array testing or all-pairs testing, more computationally complex techniques
Domain-to-range_ratio
Algorithm used for frequency estimation and radio direction finding
{\displaystyle \{\mathbf {v} _{1},\mathbf {v} _{2},\ldots ,\mathbf {v} _{M}\}} are orthogonal to each other. If the eigenvalues of R x {\displaystyle \mathbf {R} _{x}}
MUSIC_(algorithm)
Group of electrical connectors specifically aligned
interface cards. Orthogonal midplanes connect vertical cards on one side to horizontal boards on the other side. One common orthogonal midplane connects
Backplane
Color space
}} and E Q ′ {\displaystyle E_{Q}^{\prime }} are the amplitudes of the orthogonal components of the chrominance signal. To convert from FCC YIQ to RGB:
YIQ
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