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In uniform scaling with a non-zero scale factor, all non-zero vectors retain their direction (as seen from the origin), or all have the direction reversed, depending on the sign of the scaling factor. In non-uniform scaling only the vectors that belong to an eigenspace will retain their direction. A vector that is the sum of two or more non ...
Log-log transformation places numbers into a geometric domain so that proportional deviations are represented consistently, independent of the scale and units of measurement. In biology, this is appropriate because many biological phenomena (e.g., growth, reproduction, metabolism, sensation) are fundamentally multiplicative. [22]
A manifold is isotropic if the geometry on the manifold is the same regardless of direction. 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.
Isometric projection (or "isometric perspective"), a method for drawing three-dimensional objects on flat paper so that a cubical grid is projected onto an equilateral triangle grid and distances aligned with the axes are depicted at uniform scale. Isometric scaling, in biology, when changes in size during growth or over evolutionary time do ...
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry.As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the parallel postulate with an alternative, or relaxing the metric requirement.
In some physical systems, the term scaling is used interchangeably with nondimensionalization, in order to suggest that certain quantities are better measured relative to some appropriate unit. These units refer to quantities intrinsic to the system, rather than units such as SI units.
A more flexible definition of shape takes into consideration the fact that realistic shapes are often deformable, e.g. a person in different postures, a tree bending in the wind or a hand with different finger positions. One way of modeling non-rigid movements is by homeomorphisms. Roughly speaking, a homeomorphism is a continuous stretching ...
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 ...