Definition of orthogonal in English:

orthogonal

adjective ɔːˈθɒɡ(ə)n(ə)lɔrˈθɑɡənl

1Of or involving right angles; at right angles.
直角的；正交的
Example sentencesExamples
- From these beginnings he moved to prove a number of limit theorems, now known as the Szegö limit theorem, the strong Szegö limit theorem and Szegö's orthogonal polynomials and on the unit circle.
- The present experiment set out to independently manipulate beliefs and covariation information in an orthogonal design.
- Indeed, for AH and BC to be orthogonal, the ratio (H - A) / (B - C) must be purely imaginary.
- Second, geodesics are circular arcs orthogonal to the unit circle.
- Bouquet worked on differential geometry, writing on orthogonal surfaces.
- Rotations and reflections are rigid transformations (given by orthogonal mappings) and clearly transform the centroid in the asserted fashion.
- Mathematically speaking, alternate universes are orthogonal; they're located at right angles to each other.
- In addition to his work on potential theory and orthogonal set of functions he published a short paper on the problem of the maximum value a n of a positive integer belonging to a set of n positive integers whose reciprocals add to 1.
- He studied the problem of orthogonal trajectories, making important contributions by the construction of orthogonal trajectories to families of curves.
- Examples are given which illustrate how Ibrahim applied an orthogonal compression to transform a circle into an ellipse, and an oblique compression to map a hyperbola into a second hyperbola.
- Other isolated instances of orthogonal polynomials occurring in the work of various mathematicians is mentioned later.
- As we have noted above, other contributions by Steinhaus were on orthogonal series, probability theory, real functions and their applications.
- Two synchronized video cameras record orthogonal planar views of the fins at 250 images per second.
- Least square means yield values of the dependent variable for every level of each factor from an orthogonal decomposition of the information.
- Lanczos was much influenced by Fejér; he learnt from him about Fourier series, orthogonal polynomials, and interpolation.
- His research concentrated on convergence, in particular convergence of series of orthogonal functions.
- Mercer was a mathematical analyst of originality and skill; he made noteworthy advances in the theory of integral equations, and especially in the theory of the expansion of arbitrary functions in series of orthogonal functions.
- Instead of orthogonal geometry, tour guides proudly note that hardly a right-angle is to be found in the extension.
- Other methods, such as the use of orthogonal functions, may be used for creation of a surface as well.
- His doctoral thesis studied orthogonal systems of functions.
2Statistics
(of variates) statistically independent.
〔统计〕（变值）数据独立的
Example sentencesExamples
- Proteins and peptides would be more accurately defined in high-dimensional space by orthogonal axes representing truly independent characters.
- Disciplinary infractions were further summarized by entering the 18 remaining codes into a principal-components analysis using an orthogonal rotation.
- Gram is best remembered for the Gram-Schmidt orthogonalisation process which constructs an orthogonal set from an independent one.
- As a result, in populations where the two alleles at each locus are not at equal frequency, many of the genetic effects that are orthogonal in our study population are not statistically independent.
- A test of the hypothesis that ß 1 = 1 can be constructed from the orthogonal regression estimate and standard error for 1.
1. 2.1 (of an experiment) having variates which can be treated as statistically independent.
  （实验）具有数据独立的变值的
  Example sentencesExamples
  Participants always sorted on proportion in Experiment 2, with orthogonal or one-dimensional stimulus sets.
  The NMI matrix was partitioned into orthogonal patterns of amino acid variability by factor analysis.
  We can exploit the fact that the columns of these matrices must be orthogonal to reduce the number of dimensions in which to search.
  The presence of a dicentric chromosome was confirmed by Southern blot analysis of orthogonal field alternating gel electrophoresis gels.
  Taguchi first determines the control factors that go into designing a product, their interdependencies, then generates an orthogonal array specifying the number of experiments required to find the optimal solution.

Derivatives

orthogonality

noun

The assumption of orthogonality seems to present the fewest difficulties at present.
Example sentencesExamples
- These ‘Givens rotations’ are a natural perturbation because they preserve the orthogonality of the principal components.
- In DB97-13 the orthogonality of the partial great circle girdle with respect to the lineation supports the above interpretation of the apparent symmetry in the c-axis pattern.
- This is a consequence of the independent assortment of chromosomes, which results in approximate orthogonality between unlinked locations in the genome.
- When Darboux proved the orthogonality of systems of homofocal ovals, he also showed that ovals provide a geometrical interpretation of the addition theorem and that they constitute the algebraic form of the integral solution.

orthogonally

adverb ɔːˈθɒɡ(ə)n(ə)liɔrˈθɑɡ(ə)nəli

Objective focuses the exciting light on muscle, collects it, and projects fluorescent light onto the photomultipliers through orthogonally polarized analyzers.
Example sentencesExamples
- The side AB = c is taken as a reference direction in each case, and for mathematical convenience is defined such that [Theta] c is always the largest angle or C projects orthogonally onto line AB and not outside it.
- Because the two sets of antagonistic IFMs are oriented orthogonally within the thorax, contractions in one set activate the other after a short delay, and the entire system functions as a mechanical resonator.
- Also, the demographic variables are by no means guaranteed to be orthogonally varied - the distribution of geography, age, educational level, conversational topic and sex may contain some relevant partial correlations.
- The Q y axes of BChl-a in LH1 are, along with the ring, to be coupled strongly, but the orthogonally oriented Q x axes are parallel and do not overlap.
- Ethnicity was orthogonally coded by three dummy variables for four ethnic groups (non-Hispanic White, Hispanic, African American, and other).

Origin

Late 16th century: from French, based on Greek orthogōnios 'right-angled'.

Definition of orthogonal in US English:

orthogonal

adjectiveôrˈTHäɡənlɔrˈθɑɡənl

1Of or involving right angles; at right angles.
直角的；正交的
Example sentencesExamples
- The present experiment set out to independently manipulate beliefs and covariation information in an orthogonal design.
- Lanczos was much influenced by Fejér; he learnt from him about Fourier series, orthogonal polynomials, and interpolation.
- From these beginnings he moved to prove a number of limit theorems, now known as the Szegö limit theorem, the strong Szegö limit theorem and Szegö's orthogonal polynomials and on the unit circle.
- Other isolated instances of orthogonal polynomials occurring in the work of various mathematicians is mentioned later.
- His research concentrated on convergence, in particular convergence of series of orthogonal functions.
- He studied the problem of orthogonal trajectories, making important contributions by the construction of orthogonal trajectories to families of curves.
- As we have noted above, other contributions by Steinhaus were on orthogonal series, probability theory, real functions and their applications.
- Other methods, such as the use of orthogonal functions, may be used for creation of a surface as well.
- Indeed, for AH and BC to be orthogonal, the ratio (H - A) / (B - C) must be purely imaginary.
- Bouquet worked on differential geometry, writing on orthogonal surfaces.
- Second, geodesics are circular arcs orthogonal to the unit circle.
- In addition to his work on potential theory and orthogonal set of functions he published a short paper on the problem of the maximum value a n of a positive integer belonging to a set of n positive integers whose reciprocals add to 1.
- Least square means yield values of the dependent variable for every level of each factor from an orthogonal decomposition of the information.
- His doctoral thesis studied orthogonal systems of functions.
- Two synchronized video cameras record orthogonal planar views of the fins at 250 images per second.
- Instead of orthogonal geometry, tour guides proudly note that hardly a right-angle is to be found in the extension.
- Examples are given which illustrate how Ibrahim applied an orthogonal compression to transform a circle into an ellipse, and an oblique compression to map a hyperbola into a second hyperbola.
- Rotations and reflections are rigid transformations (given by orthogonal mappings) and clearly transform the centroid in the asserted fashion.
- Mercer was a mathematical analyst of originality and skill; he made noteworthy advances in the theory of integral equations, and especially in the theory of the expansion of arbitrary functions in series of orthogonal functions.
- Mathematically speaking, alternate universes are orthogonal; they're located at right angles to each other.
2Statistics
(of variates) statistically independent.
〔统计〕（变值）数据独立的
Example sentencesExamples
- Gram is best remembered for the Gram-Schmidt orthogonalisation process which constructs an orthogonal set from an independent one.
- Proteins and peptides would be more accurately defined in high-dimensional space by orthogonal axes representing truly independent characters.
- A test of the hypothesis that ß 1 = 1 can be constructed from the orthogonal regression estimate and standard error for 1.
- Disciplinary infractions were further summarized by entering the 18 remaining codes into a principal-components analysis using an orthogonal rotation.
- As a result, in populations where the two alleles at each locus are not at equal frequency, many of the genetic effects that are orthogonal in our study population are not statistically independent.
1. 2.1 (of an experiment) having variates which can be treated as statistically independent.
  （实验）具有数据独立的变值的
  Example sentencesExamples
  The NMI matrix was partitioned into orthogonal patterns of amino acid variability by factor analysis.
  Taguchi first determines the control factors that go into designing a product, their interdependencies, then generates an orthogonal array specifying the number of experiments required to find the optimal solution.
  The presence of a dicentric chromosome was confirmed by Southern blot analysis of orthogonal field alternating gel electrophoresis gels.
  Participants always sorted on proportion in Experiment 2, with orthogonal or one-dimensional stimulus sets.
  We can exploit the fact that the columns of these matrices must be orthogonal to reduce the number of dimensions in which to search.

Origin

Late 16th century: from French, based on Greek orthogōnios ‘right-angled’.

词汇	orthogonal
释义	Definition of orthogonal in English: orthogonal adjective ɔːˈθɒɡ(ə)n(ə)lɔrˈθɑɡənl 1Of or involving right angles; at right angles. 直角的；正交的 Example sentencesExamples From these beginnings he moved to prove a number of limit theorems, now known as the Szegö limit theorem, the strong Szegö limit theorem and Szegö's orthogonal polynomials and on the unit circle. The present experiment set out to independently manipulate beliefs and covariation information in an orthogonal design. Indeed, for AH and BC to be orthogonal, the ratio (H - A) / (B - C) must be purely imaginary. Second, geodesics are circular arcs orthogonal to the unit circle. Bouquet worked on differential geometry, writing on orthogonal surfaces. Rotations and reflections are rigid transformations (given by orthogonal mappings) and clearly transform the centroid in the asserted fashion. Mathematically speaking, alternate universes are orthogonal; they're located at right angles to each other. In addition to his work on potential theory and orthogonal set of functions he published a short paper on the problem of the maximum value a n of a positive integer belonging to a set of n positive integers whose reciprocals add to 1. He studied the problem of orthogonal trajectories, making important contributions by the construction of orthogonal trajectories to families of curves. Examples are given which illustrate how Ibrahim applied an orthogonal compression to transform a circle into an ellipse, and an oblique compression to map a hyperbola into a second hyperbola. Other isolated instances of orthogonal polynomials occurring in the work of various mathematicians is mentioned later. As we have noted above, other contributions by Steinhaus were on orthogonal series, probability theory, real functions and their applications. Two synchronized video cameras record orthogonal planar views of the fins at 250 images per second. Least square means yield values of the dependent variable for every level of each factor from an orthogonal decomposition of the information. Lanczos was much influenced by Fejér; he learnt from him about Fourier series, orthogonal polynomials, and interpolation. His research concentrated on convergence, in particular convergence of series of orthogonal functions. Mercer was a mathematical analyst of originality and skill; he made noteworthy advances in the theory of integral equations, and especially in the theory of the expansion of arbitrary functions in series of orthogonal functions. Instead of orthogonal geometry, tour guides proudly note that hardly a right-angle is to be found in the extension. Other methods, such as the use of orthogonal functions, may be used for creation of a surface as well. His doctoral thesis studied orthogonal systems of functions. 2Statistics (of variates) statistically independent. 〔统计〕（变值）数据独立的 Example sentencesExamples Proteins and peptides would be more accurately defined in high-dimensional space by orthogonal axes representing truly independent characters. Disciplinary infractions were further summarized by entering the 18 remaining codes into a principal-components analysis using an orthogonal rotation. Gram is best remembered for the Gram-Schmidt orthogonalisation process which constructs an orthogonal set from an independent one. As a result, in populations where the two alleles at each locus are not at equal frequency, many of the genetic effects that are orthogonal in our study population are not statistically independent. A test of the hypothesis that ß 1 = 1 can be constructed from the orthogonal regression estimate and standard error for 1. 2.1 (of an experiment) having variates which can be treated as statistically independent. （实验）具有数据独立的变值的 Example sentencesExamples Participants always sorted on proportion in Experiment 2, with orthogonal or one-dimensional stimulus sets. The NMI matrix was partitioned into orthogonal patterns of amino acid variability by factor analysis. We can exploit the fact that the columns of these matrices must be orthogonal to reduce the number of dimensions in which to search. The presence of a dicentric chromosome was confirmed by Southern blot analysis of orthogonal field alternating gel electrophoresis gels. Taguchi first determines the control factors that go into designing a product, their interdependencies, then generates an orthogonal array specifying the number of experiments required to find the optimal solution. Derivatives orthogonality noun The assumption of orthogonality seems to present the fewest difficulties at present. Example sentencesExamples These ‘Givens rotations’ are a natural perturbation because they preserve the orthogonality of the principal components. In DB97-13 the orthogonality of the partial great circle girdle with respect to the lineation supports the above interpretation of the apparent symmetry in the c-axis pattern. This is a consequence of the independent assortment of chromosomes, which results in approximate orthogonality between unlinked locations in the genome. When Darboux proved the orthogonality of systems of homofocal ovals, he also showed that ovals provide a geometrical interpretation of the addition theorem and that they constitute the algebraic form of the integral solution. orthogonally adverb ɔːˈθɒɡ(ə)n(ə)liɔrˈθɑɡ(ə)nəli Objective focuses the exciting light on muscle, collects it, and projects fluorescent light onto the photomultipliers through orthogonally polarized analyzers. Example sentencesExamples The side AB = c is taken as a reference direction in each case, and for mathematical convenience is defined such that [Theta] c is always the largest angle or C projects orthogonally onto line AB and not outside it. Because the two sets of antagonistic IFMs are oriented orthogonally within the thorax, contractions in one set activate the other after a short delay, and the entire system functions as a mechanical resonator. Also, the demographic variables are by no means guaranteed to be orthogonally varied - the distribution of geography, age, educational level, conversational topic and sex may contain some relevant partial correlations. The Q y axes of BChl-a in LH1 are, along with the ring, to be coupled strongly, but the orthogonally oriented Q x axes are parallel and do not overlap. Ethnicity was orthogonally coded by three dummy variables for four ethnic groups (non-Hispanic White, Hispanic, African American, and other). Origin Late 16th century: from French, based on Greek orthogōnios 'right-angled'. Definition of orthogonal in US English: orthogonal adjectiveôrˈTHäɡənlɔrˈθɑɡənl 1Of or involving right angles; at right angles. 直角的；正交的 Example sentencesExamples The present experiment set out to independently manipulate beliefs and covariation information in an orthogonal design. Lanczos was much influenced by Fejér; he learnt from him about Fourier series, orthogonal polynomials, and interpolation. From these beginnings he moved to prove a number of limit theorems, now known as the Szegö limit theorem, the strong Szegö limit theorem and Szegö's orthogonal polynomials and on the unit circle. Other isolated instances of orthogonal polynomials occurring in the work of various mathematicians is mentioned later. His research concentrated on convergence, in particular convergence of series of orthogonal functions. He studied the problem of orthogonal trajectories, making important contributions by the construction of orthogonal trajectories to families of curves. As we have noted above, other contributions by Steinhaus were on orthogonal series, probability theory, real functions and their applications. Other methods, such as the use of orthogonal functions, may be used for creation of a surface as well. Indeed, for AH and BC to be orthogonal, the ratio (H - A) / (B - C) must be purely imaginary. Bouquet worked on differential geometry, writing on orthogonal surfaces. Second, geodesics are circular arcs orthogonal to the unit circle. In addition to his work on potential theory and orthogonal set of functions he published a short paper on the problem of the maximum value a n of a positive integer belonging to a set of n positive integers whose reciprocals add to 1. Least square means yield values of the dependent variable for every level of each factor from an orthogonal decomposition of the information. His doctoral thesis studied orthogonal systems of functions. Two synchronized video cameras record orthogonal planar views of the fins at 250 images per second. Instead of orthogonal geometry, tour guides proudly note that hardly a right-angle is to be found in the extension. Examples are given which illustrate how Ibrahim applied an orthogonal compression to transform a circle into an ellipse, and an oblique compression to map a hyperbola into a second hyperbola. Rotations and reflections are rigid transformations (given by orthogonal mappings) and clearly transform the centroid in the asserted fashion. Mercer was a mathematical analyst of originality and skill; he made noteworthy advances in the theory of integral equations, and especially in the theory of the expansion of arbitrary functions in series of orthogonal functions. Mathematically speaking, alternate universes are orthogonal; they're located at right angles to each other. 2Statistics (of variates) statistically independent. 〔统计〕（变值）数据独立的 Example sentencesExamples Gram is best remembered for the Gram-Schmidt orthogonalisation process which constructs an orthogonal set from an independent one. Proteins and peptides would be more accurately defined in high-dimensional space by orthogonal axes representing truly independent characters. A test of the hypothesis that ß 1 = 1 can be constructed from the orthogonal regression estimate and standard error for 1. Disciplinary infractions were further summarized by entering the 18 remaining codes into a principal-components analysis using an orthogonal rotation. As a result, in populations where the two alleles at each locus are not at equal frequency, many of the genetic effects that are orthogonal in our study population are not statistically independent. 2.1 (of an experiment) having variates which can be treated as statistically independent. （实验）具有数据独立的变值的 Example sentencesExamples The NMI matrix was partitioned into orthogonal patterns of amino acid variability by factor analysis. Taguchi first determines the control factors that go into designing a product, their interdependencies, then generates an orthogonal array specifying the number of experiments required to find the optimal solution. The presence of a dicentric chromosome was confirmed by Southern blot analysis of orthogonal field alternating gel electrophoresis gels. Participants always sorted on proportion in Experiment 2, with orthogonal or one-dimensional stimulus sets. We can exploit the fact that the columns of these matrices must be orthogonal to reduce the number of dimensions in which to search. Origin Late 16th century: from French, based on Greek orthogōnios ‘right-angled’.
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