Curiously, the Fisher information metric can also be understood as the flat-space Euclidean metric, after appropriate change of variables, as described in the main article on it.
32.
A basis gives such a form ( via the dual basis ), hence when working on with a Euclidean metric and a fixed orthonormal basis, one can work with only subscripts.
33.
The Euclidean metric ( Principal Component Analysis ), the Chi-Square distance ( Correspondence Analysis ) or the Generalized Mahalanobis distance ( Discriminant Analysis ) are among the more widely used.
34.
A complex structure gives rise to a conformal structure by choosing the standard Euclidean metric given on the complex plane and transporting it to " X " by means of the charts.
35.
That is, the Fisher information metric on a statistical manifold is simply ( four times ) the Euclidean metric restricted to the positive quadrant of the sphere, after appropriate changes of variable.
36.
Because of this fact that any " natural " metric on is not especially different from the Euclidean metric, is not always distinguished from a Euclidean-space even in professional mathematical works.
37.
The Euclidean metric in the " n "-dimensional space induces a metric g = \ lambda ^ T \ lambda on the set " U ", with matrix elements
38.
Nonetheless, if a discrete space is constructed by a rectangular tiling of the plane and the Size Thesis is accepted, the Euclidean metric will be inappropriate for measuring distances on the resulting space.
39.
Rosen ( 1940 ) has proposed that at each point of space-time, there is a Euclidean metric tensor \ gamma _ { ij } in addition to the Riemannian metric tensor g _ { ij }.
40.
Then " f " satisfies ( ) precisely when it is a conformal transformation from " D " equipped with this metric to the domain " D " 2 equipped with the standard Euclidean metric.
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