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  2. Matrix similarity - Wikipedia

    en.wikipedia.org/wiki/Matrix_similarity

    This means that one may use Jordan forms that only exist over a larger field to determine whether the given matrices are similar. In the definition of similarity, if the matrix P can be chosen to be a permutation matrix then A and B are permutation-similar; if P can be chosen to be a unitary matrix then A and B are unitarily equivalent.

  3. Similarity invariance - Wikipedia

    en.wikipedia.org/wiki/Similarity_invariance

    In linear algebra, similarity invariance is a property exhibited by a function whose value is unchanged under similarities of its domain. That is, f {\displaystyle f} is invariant under similarities if f ( A ) = f ( B − 1 A B ) {\displaystyle f(A)=f(B^{-1}AB)} where B − 1 A B {\displaystyle B^{-1}AB} is a matrix similar to A .

  4. Similarity measure - Wikipedia

    en.wikipedia.org/wiki/Similarity_measure

    Clustering or Cluster analysis is a data mining technique that is used to discover patterns in data by grouping similar objects together. It involves partitioning a set of data points into groups or clusters based on their similarities. One of the fundamental aspects of clustering is how to measure similarity between data points.

  5. Relationships among probability distributions - Wikipedia

    en.wikipedia.org/wiki/Relationships_among...

    X (X) is a standard uniform (0,1) random variable; If X is a normal (μ, σ 2) random variable then e X is a lognormal (μ, σ 2) random variable. Conversely, if X is a lognormal (μ, σ 2) random variable then log X is a normal (μ, σ 2) random variable. If X is an exponential random variable with mean β, then X 1/γ is a Weibull (γ, β ...

  6. Self-similarity - Wikipedia

    en.wikipedia.org/wiki/Self-similarity

    In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e., the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines , are statistically self-similar: parts of them show the same statistical properties at many scales. [ 2 ]

  7. Isotropy - Wikipedia

    en.wikipedia.org/wiki/Isotropy

    A similar concept is homogeneity. Isotropic quadratic form A quadratic form q is said to be isotropic if there is a non-zero vector v such that q(v) = 0; such a v is an isotropic vector or null vector. In complex geometry, a line through the origin in the direction of an isotropic vector is an isotropic line. Isotropic coordinates

  8. Uniformitarianism - Wikipedia

    en.wikipedia.org/wiki/Uniformitarianism

    Hutton's Unconformity at Jedburgh. Above: John Clerk of Eldin's 1787 illustration. Below: 2003 photograph. Uniformitarianism, also known as the Doctrine of Uniformity or the Uniformitarian Principle, [1] is the assumption that the same natural laws and processes that operate in our present-day scientific observations have always operated in the universe in the past and apply everywhere in the ...

  9. Homogeneity and heterogeneity (statistics) - Wikipedia

    en.wikipedia.org/wiki/Homogeneity_and...

    They relate to the validity of the often convenient assumption that the statistical properties of any one part of an overall dataset are the same as any other part. In meta-analysis, which combines the data from several studies, homogeneity measures the differences or similarities between the several studies (see also Study heterogeneity).

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