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Let X be an affine space over a field k, and V be its associated vector space. An affine transformation is a bijection f from X onto itself that is an affine map; this means that a linear map g from V to V is well defined by the equation () = (); here, as usual, the subtraction of two points denotes the free vector from the second point to the first one, and "well-defined" means that ...
In mathematics, and especially in category theory, a commutative diagram is a diagram of objects, also known as vertices, and morphisms, also known as arrows or edges, such that when selecting two objects any directed path through the diagram leads to the same result by composition.
In mathematics, self-affinity is a feature of a fractal whose pieces are scaled by different amounts in the x- and y-directions. This means that to appreciate the self similarity of these fractal objects, they have to be rescaled using an anisotropic affine transformation .
Finite examples in dimension 2 (finite affine planes) have been valuable in the study of configurations in infinite affine spaces, in group theory, and in combinatorics. Despite being less general than the configurational approach, the other approaches discussed have been very successful in illuminating the parts of geometry that are related to ...
These are examples of affine connections. There is also a concept of projective connection, of which the Schwarzian derivative in complex analysis is an instance. More generally, both affine and projective connections are types of Cartan connections. Using principal bundles, a connection can be realized as a Lie algebra-valued differential form.
Origins from Alice's and Bob's perspectives. Vector computation from Alice's perspective is in red, whereas that from Bob's is in blue. The following characterization may be easier to understand than the usual formal definition: an affine space is what is left of a vector space after one has forgotten which point is the origin (or, in the words of the French mathematician Marcel Berger, "An ...
Affinity wall diagram. The affinity diagram is a business tool used to organize ideas and data. It is one of the Seven Management and Planning Tools.People have been grouping data into groups based on natural relationships for thousands of years; however, the term affinity diagram was devised by Jiro Kawakita in the 1960s [1] and is sometimes referred to as the KJ Method.
Affinity diagram. Affinity diagrams are a special kind of brainstorming tool that organize large amount of disorganized data and information into groupings based on natural relationships. It was created in the 1960s by the Japanese anthropologist Jiro Kawakita. It is also known as KJ diagram, after Jiro Kawakita. An affinity diagram is used when: