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Point groups are used to describe the symmetries of geometric figures and physical objects such as molecules . Each point group can be represented as sets of orthogonal matrices M that transform point x into point y according to y = Mx. Each element of a point group is either a rotation ( determinant of M = 1 ), or it is a reflection or ...
Transformation matrix. In linear algebra, linear transformations can be represented by matrices. If is a linear transformation mapping to and is a column vector with entries, then. for some matrix , called the transformation matrix of . [citation needed] Note that has rows and columns, whereas the transformation is from to .
O h, (*432) [4,3] =. Icosahedral symmetry. I h, (*532) [5,3] =. In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere. It is a subgroup of the orthogonal group O (3), the group of all isometries that leave the origin fixed, or ...
Antisolar point. The antisolar point is the abstract point on the celestial sphere directly opposite the Sun from an observer's perspective. [1] This means that the antisolar point lies above the horizon when the Sun is below it, and vice versa. On a sunny day, the antisolar point can be easily found; it is located within the shadow of the ...
Lambertian reflectance is the property that defines an ideal "matte" or diffusely reflecting surface. The apparent brightness of a Lambertian surface to an observer is the same regardless of the observer's angle of view. [1] More precisely, the reflected radiant intensity obeys Lambert's cosine law, which makes the reflected radiance the same ...
Reflection formula. In mathematics, a reflection formula or reflection relation for a function f is a relationship between f ( a − x) and f ( x ). It is a special case of a functional equation. It is common in mathematical literature to use the term "functional equation" for what are specifically reflection formulae.
Total internal reflection fluorescence microscope. A total internal reflection fluorescence microscope ( TIRFM) is a type of microscope with which a thin region of a specimen, usually less than 200 nanometers can be observed. TIRFM is an imaging modality which uses the excitation of fluorescent cells in a thin optical specimen section that is ...
