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Data analysis process
In statistics, econometrics and related fields, multidimensional analysis (MDA) is a data analysis process that groups data into two categories: data dimensions
Multidimensional_analysis
Processing mode
emerging, such as agriculture. OLAP tools enable users to analyse multidimensional data interactively from multiple perspectives. OLAP consists of three
Online_analytical_processing
Set of related ordination techniques used in information visualization
Multidimensional scaling (MDS) is a means of visualizing the level of similarity of individual cases of a data set. MDS is used to translate distances
Multidimensional_scaling
Reporting tool
JasperReports is an open source Java reporting tool that can write to a variety of targets, such as: screen, a printer, into PDF, HTML, Microsoft Excel
JasperReports
Tool for digital signal processing
and decoding of multidimensional signals. The general multidimensional filter bank (Figure 7) can be represented by a pair of analysis and synthesis polyphase
Filter_bank
Mathematical analysis of frequency content of signals
In mathematical analysis and applications, multidimensional transforms are used to analyze the frequency content of signals in a domain of two or more
Multidimensional_transform
Analysis of datasets using techniques from topology
low-dimensional structure from the data set, such as principal component analysis and multidimensional scaling. However, it is important to note that the problem itself
Topological_data_analysis
Method of data analysis
Nicolelis, Miguel (1999). "Principal component analysis of neuronal ensemble activity reveals multidimensional somatosensory representations". Journal of
Principal_component_analysis
Simultaneous observation and analysis of more than one outcome variable
Probability computations of multidimensional regions The exploration of data structures and patterns Multivariate analysis can be complicated by the desire
Multivariate_statistics
Analysis of the dimensions of different physical quantities
ISBN 978-0-89871-336-7 As postscript Hart, George W. (1995), Multidimensional Analysis: Algebras and Systems for Science and Engineering, Springer-Verlag
Dimensional_analysis
Networks with multiple kinds of relations
model real-world systems as multidimensional networks have yielded valuable insight in the fields of social network analysis, economics, urban and international
Multidimensional_network
Property of a mathematical space
Dimension tables Dimensional analysis Flatland Hyperspace (disambiguation) Intrinsic dimension Mean dimension Multidimensional analysis Space-filling curve Technical
Dimension
Statistical method
individuals and then a regression is run over these two dimensions. Multidimensional analysis is an econometric method in which data are collected over more
Panel_analysis
Formula and data query language
part, an evolution of the Multidimensional Expression (MDX) language developed by Microsoft for Analysis Services multidimensional models (often called cubes)
Data_Analysis_Expressions
American business intelligence company
California, was founded by Praveen Kankariya. Kyvos provides multidimensional analysis at scale on cloud platforms and was launched officially in June
Kyvos
Compressed form of cannabis resin
Marchini, Céline Charvoz, Laurence Dujourdy and Nicolas Baldovini (Multidimensional analysis of cannabis volatile constituents: Identification of 5
Hashish
Range of poverty indicators
Multidimensional Poverty Indices use a range of indicators (monetary, health, education and others) to calculate a summary poverty figure for a given population
Multidimensional Poverty Index
Multidimensional_Poverty_Index
Wavelet analysis is extended for multidimensional signal processing as well. This article introduces a few methods for wavelet synthesis and analysis for
Wavelet for multidimensional signals analysis
Wavelet_for_multidimensional_signals_analysis
Spectroscopic technique
Urban; Thomas Schmid; Andrea Amantonico; Renato Zenobi (2011). "Multidimensional Analysis of Single Algal Cells by Integrating Microspectroscopy with Mass
Raman_spectroscopy
Method used in statistics, pattern recognition, and other fields
Factor analysis Kernel Fisher discriminant analysis Logit (for logistic regression) Linear regression Multiple discriminant analysis Multidimensional scaling
Linear_discriminant_analysis
Signal processing algorithm
functions combined with the Hilbert spectral analysis, known as the Hilbert–Huang transform (HHT). The multidimensional EMD extends the 1-D EMD algorithm into
Multidimensional empirical mode decomposition
Multidimensional_empirical_mode_decomposition
American geometer (born 1955)
the online publication Encyclopedia of Polyhedra, the textbook Multidimensional Analysis, and the instruction book Zome Geometry. He has also published
George_W._Hart
American politician, astronaut and naval officer (born 1964)
B. E.; De Vivo, I. (April 12, 2019). "The NASA Twins Study: A multidimensional analysis of a year-long human spaceflight". Science. 364 (6436) eaau8650
Mark_Kelly
Analysis of social structures using network and graph theory
"SIM: A dynamic multidimensional visualization method for social networks". PsychNology Journal. 6 (3): 291–320. "Network Analysis and Modeling (CSCI
Social_network_analysis
Psychological measurement instrument
The Multidimensional Scale of Perceived Social Support (MSPSS) is a widely used psychological measurement instrument to assess an individual's perceived
Multidimensional Scale of Perceived Social Support
Multidimensional_Scale_of_Perceived_Social_Support
Words that imitate the sound they describe
1177/0142723714550110. S2CID 147624168. Osaka, Naoyuki (1990). "Multidimensional Analysis of Onomatopoeia – A note to make sensory scale from word". Studia
Onomatopoeia
Approach of analyzing data sets in statistics
versions of these plots Dimensionality reduction: Multidimensional scaling Principal component analysis (PCA) Multilinear PCA Nonlinear dimensionality reduction
Exploratory_data_analysis
American psychologist (1928–1971)
the Electronic Profile Analyzing Computer (EPAC), to perform multidimensional analysis for psychometrics. He used it between 1951 and 1953 to analyze
Frank_Rosenblatt
Fast Analysis of Shared Multidimensional Information (FASMI) is an alternative term for OLAP. The term was coined by Nigel Pendse of The OLAP Report (now
FASMI
Online analytical processing (OLAP) and data mining tool in Microsoft SQL Server
Services and Analysis Services. Analysis Services includes a group of OLAP and data mining capabilities and comes in two flavors multidimensional and tabular
Microsoft_Analysis_Services
Family of numerical optimization methods
best match (the solution that has the lowest error value) in a multidimensional analysis space of possibilities. The name "pattern search" was coined by
Pattern_search_(optimization)
Topics referred to by the same term
two-dimensional array optimized for multidimensional analysis Cubes (OLAP server), a light-weight open source multidimensional modelling and OLAP toolkit Power
Cube_(disambiguation)
Overview of and topical guide to machine learning
(LDA) Multidimensional scaling (MDS) Non-negative matrix factorization (NMF) Partial least squares regression (PLSR) Principal component analysis (PCA)
Outline_of_machine_learning
Numerical method for solving physical or engineering problems
restricted to triangles (tetrahedra in 3-d or higher-order simplexes in multidimensional spaces). Still, it can be defined on quadrilateral subdomains (hexahedra
Finite_element_method
Study of uncertainty in the output of a mathematical model or system
large number of uncertain inputs. Sensitivity analysis is essentially the exploration of the multidimensional input space, which grows exponentially in size
Sensitivity_analysis
Research project of the health effects of being in space long term
Francine E.; et al. (12 April 2019). "The NASA Twins Study: A multidimensional analysis of a year-long human spaceflight". Science. 364 (6436) eaau8650
ISS_year-long_mission
Grouping a set of objects by similarity
Neighbourhood components analysis Latent class analysis Affinity propagation Dimension reduction Principal component analysis Multidimensional scaling Cluster-weighted
Cluster_analysis
Algebraic object with geometric applications
levels of abstraction. A tensor may be represented as a (potentially multidimensional) array. Just as a vector in an n-dimensional space is represented by
Tensor
processing, multidimensional signal processing covers all signal processing done using multidimensional signals and systems. While multidimensional signal
Multidimensional signal processing
Multidimensional_signal_processing
Method of deriving an ontology
use standard definitions and algorithms from multidimensional concept analysis for computing multidimensional clusters. In the theory of knowledge spaces
Formal_concept_analysis
German state from 1918 to 1933
(2014). Access to Justice in Transnational B2C E-Commerce. A Multidimensional Analysis of Consumer Protection Mechanisms. New York: Springer International
Weimar_Republic
In digital signal processing, multidimensional sampling is the process of converting a function of a multidimensional variable into a discrete collection
Multidimensional_sampling
Turkish engineer and politician (born 1975)
Technical University (METU) in Turkey, focusing his research on "A Multidimensional Analysis of Turkish-German Low Carbon Energy Transitions." Bayraktar has
Alparslan_Bayraktar
Computational technique
now widely employed to accelerate multidimensional DSP, such as image processing, video codecs, radar signal analysis, sonar signal processing, and ultrasound
Multidimensional DSP with GPU acceleration
Multidimensional_DSP_with_GPU_acceleration
Discrete Fourier transform algorithm
Multidimensional Signals Fast Fourier Transform Telescope Fast Walsh–Hadamard transform Generalized distributive law Least-squares spectral analysis Multidimensional
Fast_Fourier_transform
Technique used in public administration
Policy analysis or public policy analysis is a technique used in the public administration sub-field of political science to enable civil servants, nonprofit
Policy_analysis
OLAP query language
Multidimensional Expressions (MDX) is a query language for online analytical processing (OLAP) using a database management system. Much like SQL, it is
MultiDimensional_eXpressions
Optimization problem in computer science
inner-product search MinHash Multidimensional analysis Nearest-neighbor interpolation Neighbor joining Principal component analysis Range search Similarity
Nearest_neighbor_search
1971 arrest of Bangladeshi statesman
যুদ্ধাপরাধ: বহুমাত্রিক বিশ্লেষণ [War Crimes in Bangladesh: A Multidimensional Analysis] (in Bengali). Eastern Publications. p. 98. Sayeed 2011, pp. 36
Arrest of Sheikh Mujibur Rahman
Arrest_of_Sheikh_Mujibur_Rahman
Factorial method
ordination used to simplify multidimensional data structures. MFA treats all involved tables in the same way (symmetrical analysis). It may be seen as an extension
Multiple_factor_analysis
Computer program for working with tabular data
reference each other with user-defined variable names and to perform multidimensional analysis and massive, but easily editable consolidations. Spreadsheets
Spreadsheet
Form of acquaintance rape and dating violence
"Rape Myth Acceptance and Sociodemographic Characteristics: A Multidimensional Analysis". Sex Roles. 36 (11–12): 693–707. doi:10.1023/A:1025671021697
Date_rape
Approach of psychological scientific study
"Well-being is more than happiness and life satisfaction: a multidimensional analysis of 21 countries". Health and Quality of Life Outcomes. 18 (1):
Positive_psychology
concepts, principles and applications of Multirate filter banks and Multidimensional Directional filter banks. Linear time-invariant systems typically operate
Multirate filter bank and multidimensional directional filter banks
Multirate_filter_bank_and_multidimensional_directional_filter_banks
Sequence of data points over time
series is one type of panel data. Panel data is the general class, a multidimensional data set, whereas a time series data set is a one-dimensional panel
Time_series
Peacekeeping force in Mali after the Tuareg rebellion of 2012
The United Nations Multidimensional Integrated Stabilization Mission in Mali (French: Mission multidimensionnelle intégrée des Nations Unies pour la stabilisation
United Nations Multidimensional Integrated Stabilization Mission in Mali
United_Nations_Multidimensional_Integrated_Stabilization_Mission_in_Mali
Projection of data onto lower-dimensional manifolds
manifolds in the gait analysis, a multi-layer joint gait-pose manifolds was proposed. Relational perspective map is a multidimensional scaling algorithm.
Nonlinear dimensionality reduction
Nonlinear_dimensionality_reduction
Extremely large or complex datasets
Visualization, such as charts, graphs, and other displays of the data Multidimensional big data can also be represented as OLAP data cubes or, mathematically
Big_data
Business intelligence suite
and search for background information about an event or action. Multidimensional analysis allows identifying trends and understanding of anomalies or deviations
IBM_Cognos_Analytics
Theorem in dimensional analysis
(PDF). NTNU. Retrieved April 9, 2007. Hart, George W. (1995). Multidimensional Analysis: Algebras and Systems for Science and Engineering. Springer.
Buckingham_pi_theorem
Type of housing for older adults
BJ (March 2000). "Quality of life in assisted living homes: a multidimensional analysis". The Journals of Gerontology. Series B, Psychological Sciences
Independent_senior_living
Notion in healthcare
now usually assessed using patient questionnaires. These are often multidimensional and cover physical, social, emotional, cognitive, work- or role-related
Quality_of_life_(healthcare)
"typical" observations (cluster centers), it seeks extremal points in the multidimensional data, the "archetypes". The archetypes are convex combinations of observations
Archetypal_analysis
Generalization of the one-dimensional normal distribution to higher dimensions
distribution function (cdf) in dimension 1 can be extended in two ways to the multidimensional case, based on rectangular and ellipsoidal regions. The first way is
Multivariate normal distribution
Multivariate_normal_distribution
Branch of political science
non-governmental actors such as NGOs or the media. Multilevel and Multidimensional approach - In this model, scholars study particular aspects of foreign
Foreign_policy_analysis
Crystalline materials consisting of a single layer of atoms
Qianhui; Zheng, Changxi; Fuhrer, Michael; Davis, Jeffrey (2021). "Multidimensional analysis of excitonic spectra of monolayers of tungsten disulphide: toward
Single-layer_materials
District and municipality in İzmir, Turkey
ISBN 0871691272. p. 239. Lieberman, 2013: pp. 79–80 Erol, Emre (2012). "A Multidimensional Analysis of the Events in Eski Foça (Παλαιά Φώκαια) on the period of Summer
Foça
Multidimensional modulation (MD modulation) is modifying or multiplying an MD signal (typically sinusoidal and referred to as the carrier signal) with
Multidimensional_modulation
Process of reducing the number of random variables under consideration
in principal component analysis (PCA), but many nonlinear dimensionality reduction techniques also exist. For multidimensional data, tensor representation
Dimensionality_reduction
Multidimensional data array organized for rapid analysis
Data Mining Extensions Fast Analysis of Shared Multidimensional Information Multidimensional Expressions XML for Analysis Gray, Jim; Bosworth, Adam; Layman
OLAP_cube
Timeout, Catalog name, etc. The result of Execute command could be Multidimensional Dataset or Tabular Rowset. Discover method was designed to model all
XML_for_Analysis
Type of unpleasant bodily feeling
(45–74mm) and severe pain (75–100mm).[check quotation syntax] The Multidimensional Pain Inventory (MPI) is a questionnaire designed to assess the psychosocial
Pain
Genocide campaign in the Ottoman Empire
Violent Turkification". In Schaller & Zimmerer (2009), pp. 34 ff. A Multidimensional Analysis of the Events in Eski Foça (Παλαιά Φώκαια) on the period of Summer
Greek_genocide
Agreement between two or more parties
Haugland. "Predicting and measuring alliance performance: A multidimensional analysis." Strategic Management Journal 29.5 (2008): 545–556. Niederkofler
Strategic_alliance
Medical issues associated with spaceflight
Francine E.; et al. (12 April 2019). "The NASA Twins Study: A multidimensional analysis of a year-long human spaceflight". Science. 364 (6436) eaau8650
Effect of spaceflight on the human body
Effect_of_spaceflight_on_the_human_body
Mapping function that preserves data point locality
curve, Morton space-filling curve, Morton order or Morton code map multidimensional data to one dimension while preserving locality of the data points
Z-order_curve
Parameter-free superresolution algorithm
SAMV (iterative sparse asymptotic minimum variance) is a parameter-free superresolution algorithm for the linear inverse problem in spectral estimation
SAMV_(algorithm)
trimming system operates continually on seagoing vessels, and uses multidimensional analysis of real-time data on vessel attitude collected automatically from
Dynamic_trimming
Cellular stress response
Kries K, Brown CM, Augsornworawat P, et al. (September 2022). "Multidimensional analysis and therapeutic development using patient iPSC-derived disease
Unfolded_protein_response
Way of inferring information from cross-covariance matrices
In statistics, canonical-correlation analysis (CCA), also called canonical variates analysis, is a way of inferring information from cross-covariance
Canonical_correlation
Technique in natural language processing
Latent semantic analysis (LSA) is a technique in natural language processing, in particular distributional semantics, of analyzing relationships between
Latent_semantic_analysis
Fundamental theorem in probability theory and statistics
these random vectors are independent and identically distributed. The multidimensional central limit theorem states that when scaled, sums converge to a multivariate
Central_limit_theorem
Type of operator in Fourier analysis
701–703, Zbl 0073.08402 (in Russian). Mikhlin, Solomon G. (1965), Multidimensional singular integrals and integral equations, International Series of
Multiplier_(Fourier_analysis)
Investigative data-analysis technique
In network theory, link analysis is a data-analysis technique used to evaluate relationships between nodes. Relationships may be identified among various
Link_analysis
Algorithm for finding zeros of functions
In numerical analysis, the Newton–Raphson method, also known simply as Newton's method, named after Isaac Newton and Joseph Raphson, is a root-finding
Newton's_method
Function in discrete mathematics
Generalizations of Pauli matrices Least-squares spectral analysis List of Fourier-related transforms Multidimensional transform Zak transform Quantum Fourier transform
Discrete_Fourier_transform
Executed Chinese serial killer
execution was not specified. List of serial killers in China A Multidimensional Analysis of the Subjective Mental State of Crime——Taking Zhou Youping's
Zhou_Youping
two-dimensional function with many local minima Shekel function — multimodal and multidimensional Mathematical Optimization Society Numerical integration — the numerical
List of numerical analysis topics
List_of_numerical_analysis_topics
Curve', graphically showing the potential margin of an organisation. "Multidimensional Costing – Value to Use". valuetouse.com. Retrieved 5 May 2017.
Profitability_analysis
mechanisms. Madagascar, an open-source software package for multidimensional data analysis and reproducible computational experiments. mlpack is an open-source
List of numerical-analysis software
List_of_numerical-analysis_software
Software extending the spreadsheet paradigm
reference each other with user-defined variable names, and to perform multidimensional analysis and massive, but easily editable consolidations. Javelin encourages
Javelin_Software
Mass cytometry application to quantify labeled cell targets
populations dimensionality reduction algorithms are often used. Several multidimensional analysis clustering algorithms are common. Popular tools include tSNE,
CyTOF
1914 killing of Greeks in the Ottoman Empire
Bjornlund, 2013: p. 47 Smith, 1998: p. 32 Erol, Emre (2012). "A multidimensional analysis of the events in Eski Foça (Παλαιά Φώκαια) on the period of summer
Massacre_of_Phocaea
Black feminist lesbian organization
'essentialist' appeals and doctrines..." The Collective developed a multidimensional analysis recognizing a "simultaneity of oppressions", refusing to rank
Combahee_River_Collective
Pugh concept selection
investment options, vendor options, product options or any other set of multidimensional entities. A basic decision matrix consists of establishing a set of
Decision-matrix_method
British mathematician
S2CID 124324198. Gowers, W. T. (2007). "Hypergraph regularity and the multidimensional Szemerédi theorem". Ann. of Math. 166 (3): 897–946. arXiv:0710.3032
Timothy_Gowers
Theory and technique of psychological measurement
finding objects that are like each other. Factor analysis, multidimensional scaling, and cluster analysis are all multivariate descriptive methods used to
Psychometrics
Large-scale study of proteins
"Evaluation of multidimensional chromatography coupled with tandem mass spectrometry (LC/LC-MS/MS) for large-scale protein analysis: the yeast proteome"
Proteomics
Technique used to study & characterize materials
both frequency studies and temperature studies, there is interest in multidimensional studies, where temperature sweeps are conducted at a variety of frequencies
Dynamic_mechanical_analysis
Mathematical operation in signal processing
In signal processing, multidimensional discrete convolution refers to the mathematical operation between two functions f and g on an n-dimensional lattice
Multidimensional discrete convolution
Multidimensional_discrete_convolution
MULTIDIMENSIONAL ANALYSIS
MULTIDIMENSIONAL ANALYSIS
Girl/Female
Hindu
Analysis
Girl/Female
Tamil
Sameksha | ஸமேகà¯à®·à®¾
Analysis
Sameksha | ஸமேகà¯à®·à®¾
Girl/Female
Indian
Analysis
Girl/Female
Hindu
Analysis
Girl/Female
Tamil
Sameeksha | ஸமீகà¯à®·à®¾Â
Analysis
Sameeksha | ஸமீகà¯à®·à®¾Â
Girl/Female
Hindu
Analysis
Girl/Female
Muslim
Analysis
Girl/Female
Tamil
Sumiksha | ஸà¯à®®à¯€à®•à¯à®·à®¾Â
Close inspection, A review, Analysis
Sumiksha | ஸà¯à®®à¯€à®•à¯à®·à®¾Â
Girl/Female
Indian, Telugu
Review; Analysis
Girl/Female
Hindu
Close inspection, A review, Analysis
Girl/Female
Tamil
Samiksha | ஸமீகà¯à®·à®¾
Analysis
MULTIDIMENSIONAL ANALYSIS
MULTIDIMENSIONAL ANALYSIS
Boy/Male
Gujarati, Hindu, Indian
Simple
Surname or Lastname
English
English : variant of Whitelaw.
Boy/Male
Tamil
Without form
Male
English
Anglicized form of Hebrew Galiyl, GALILEE means "rolling, turning" or "circuit, region, ring." In the bible, this is the name of a circuit or ring (Galilee) of the Gentiles. Not used as a personal name.
Female
English
Feminine pet form of Scottish unisex Leslie, LESSIE means "garden of hollies."
Female
German
Pet form of German Elisabeth, LIESE means "God is my oath."Â
Boy/Male
Hindu
Sight, Handsome, Lord Krishna
Male
Spanish
Spanish name derived from Latin Salvator, SALVADOR means "savior."
Surname or Lastname
English
English : habitational name from any of the numerous places named with Old English cnihta, genitive plural of cniht ‘servant’, ‘retainer’ + tūn ‘enclosure’, ‘settlement’.
Girl/Female
English, Traditional
Shining
MULTIDIMENSIONAL ANALYSIS
MULTIDIMENSIONAL ANALYSIS
MULTIDIMENSIONAL ANALYSIS
MULTIDIMENSIONAL ANALYSIS
MULTIDIMENSIONAL ANALYSIS
n.
Chemical analysis.
a.
Of or pertaining to the spectrum; made by the spectrum; as, spectral colors; spectral analysis.
n.
The science of blowpipe analysis.
n.
Anything which resounds; specifically, a vessel in the form of a cylinder open at one end, or a hollow ball of brass with two apertures, so contrived as to greatly intensify a musical tone by its resonance. It is used for the study and analysis of complex sounds.
v. t.
To consider by a separate act of attention or analysis.
n.
An instrument for ascertaining the strength of an indigo solution, as in volumetric analysis.
n.
A rare metallic element of the boron group, whose existence was predicted under the provisional name ekaboron by means of the periodic law, and subsequently discovered by spectrum analysis in certain rare Scandinavian minerals (euxenite and gadolinite). It has not yet been isolated. Symbol Sc. Atomic weight 44.
n.
The separation of a compound substance, by chemical processes, into its constituents, with a view to ascertain either (a) what elements it contains, or (b) how much of each element is present. The former is called qualitative, and the latter quantitative analysis.
n.
That which indicates the condition of acidity, alkalinity, or the deficiency, excess, or sufficiency of a standard reagent, by causing an appearance, disappearance, or change of color, as in titration or volumetric analysis.
n.
Analysis into primary or elemental parts.
n.
The combination of separate elements of thought into a whole, as of simple into complex conceptions, species into genera, individual propositions into systems; -- the opposite of analysis.
n.
Any original inherent constituent which characterizes a substance, or gives it its essential properties, and which can usually be separated by analysis; -- applied especially to drugs, plant extracts, etc.
n.
A rare alkaline metal found in mineral water; -- so called from the two characteristic blue lines in its spectrum. It was the first element discovered by spectrum analysis, and is the most strongly basic and electro-positive substance known. Symbol Cs. Atomic weight 132.6.
n.
An apparatus for determining the amount of nitrogen or some of its compounds in any substance subjected to analysis; an azotometer.
n.
The science of spectrum analysis in any or all of its relations and applications.
v. t.
To reduce to a normal standard; to calculate or adjust the strength of, by means of, and for uses in, analysis.
n.
The art or process of making a compound by putting the ingredients together, as contrasted with analysis; thus, water is made by synthesis from hydrogen and oxygen; hence, specifically, the building up of complex compounds by special reactions, whereby their component radicals are so grouped that the resulting substances are identical in every respect with the natural articles when such occur; thus, artificial alcohol, urea, indigo blue, alizarin, etc., are made by synthesis.
a.
Incapable of further analysis; incapable of further division or separation; constituent; elemental; as, an ultimate constituent of matter.
v. t.
A very small quantity of an element or compound in a given substance, especially when so small that the amount is not quantitatively determined in an analysis; -- hence, in stating an analysis, often contracted to tr.
n.
In the quaternion analysis, a quantity that has magnitude, but not direction; -- distinguished from a vector, which has both magnitude and direction.