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The polar decomposition factors a matrix into a pair, one of which is the unique closest orthogonal matrix to the given matrix, or one of the closest if the given matrix is singular. (Closeness can be measured by any matrix norm invariant under an orthogonal change of basis, such as the spectral norm or the Frobenius norm.)
Grosskopf and Nagel's investigation also revealed that most players do not choose 0 the first time they play this game. Instead, they realise that 0 is the Nash Equilibrium after some repetitions. [14] A study by Nagel reported an average initial choice of around 36. This corresponds to approximately two levels of k-level reasoning. [15]
In botanical nomenclature, an orthographical variant (abbreviated orth. var.) is a variant spelling of the same name. For example, Hieronima [ 1 ] and Hyeronima [ 2 ] are orthographical variants of Hieronyma .
The Catholic Church and the Eastern Orthodox Church have been in a state of official schism from one another since the East–West Schism of 1054. This schism was caused by historical and language differences, and the ensuing theological differences between the Western and Eastern churches.
The closest pair of points problem or closest pair problem is a problem of computational geometry: given points in metric space, find a pair of points with the smallest distance between them. The closest pair problem for points in the Euclidean plane [ 1 ] was among the first geometric problems that were treated at the origins of the systematic ...
In a minor key, the closely related keys are the parallel major, mediant or relative major, the subdominant, the minor dominant, the submediant, and the subtonic.In the key of A minor, when we translate them to keys, we get:
Zhang [4] proposes a modified k-d tree algorithm for efficient closest point computation. In this work a statistical method based on the distance distribution is used to deal with outliers, occlusion, appearance, and disappearance, which enables subset-subset matching.
The closeness of a match is measured in terms of the number of primitive operations necessary to convert the string into an exact match. This number is called the edit distance between the string and the pattern. The usual primitive operations are: [1] insertion: cot → coat; deletion: coat → cot; substitution: coat → cost