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  2. Matrix similarity - Wikipedia

    en.wikipedia.org/wiki/Matrix_similarity

    Similarity is an equivalence relation on the space of square matrices. Because matrices are similar if and only if they represent the same linear operator with respect to (possibly) different bases, similar matrices share all properties of their shared underlying operator: Rank; Characteristic polynomial, and attributes that can be derived from it:

  3. Self-similarity - Wikipedia

    en.wikipedia.org/wiki/Self-similarity

    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] Self-similarity is a typical property of fractals. Scale invariance is an exact form of self-similarity where at any magnification there is a smaller piece of the object that is similar to ...

  4. Similarity invariance - Wikipedia

    en.wikipedia.org/wiki/Similarity_invariance

    A more colloquial phrase that means the same thing as similarity invariance is "basis independence", since a matrix can be regarded as a linear operator, written in a certain basis, and the same operator in a new basis is related to one in the old basis by the conjugation , where is the transformation matrix to the new basis.

  5. Homogeneity and heterogeneity - Wikipedia

    en.wikipedia.org/wiki/Homogeneity_and_heterogeneity

    Homogeneity and heterogeneity; only ' b ' is homogeneous Homogeneity and heterogeneity are concepts relating to the uniformity of a substance, process or image.A homogeneous feature is uniform in composition or character (i.e., color, shape, size, weight, height, distribution, texture, language, income, disease, temperature, radioactivity, architectural design, etc.); one that is heterogeneous ...

  6. Homogeneity and heterogeneity (statistics) - Wikipedia

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

    For example, considerations of homoscedasticity examine how much the variability of data-values changes throughout a dataset. However, questions of homogeneity apply to all aspects of the statistical distributions, including the location parameter. Thus, a more detailed study would examine changes to the whole of the marginal distribution.

  7. Ratio of uniforms - Wikipedia

    en.wikipedia.org/wiki/Ratio_of_uniforms

    The ratio of uniforms is a method initially proposed by Kinderman and Monahan in 1977 [1] for pseudo-random number sampling, that is, for drawing random samples from a statistical distribution. Like rejection sampling and inverse transform sampling, it is an exact simulation method. The basic idea of the method is to use a change of variables ...

  8. Similarity transformation - Wikipedia

    en.wikipedia.org/wiki/Similarity_transformation

    Similarity transformation may refer to: Similarity (geometry) , for shape-preserving transformations Matrix similarity , for matrix transformations of the form A → P −1 AP

  9. Discrete uniform distribution - Wikipedia

    en.wikipedia.org/wiki/Discrete_uniform_distribution

    The problem of estimating the maximum of a discrete uniform distribution on the integer interval [,] from a sample of k observations is commonly known as the German tank problem, following the practical application of this maximum estimation problem, during World War II, by Allied forces seeking to estimate German tank production.

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