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In quantum mechanics, a density matrix (or density operator) is a matrix that describes an ensemble [1] of physical systems as quantum states (even if the ensemble contains only one system). It allows for the calculation of the probabilities of the outcomes of any measurements performed upon the systems of the ensemble using the Born rule .
Scene from the 1990 film Total Recall. Historians of film note that the trope of a "red pill" as decisive in a return to reality made its first appearance in the 1990 film Total Recall, which has a scene where the hero (played by Arnold Schwarzenegger) is asked to swallow a red pill in order to symbolize his desire to return to reality from a dream-like fantasy.
D&D co-creator Gary Gygax credited the inspiration for the alignment system to the fantasy stories of Michael Moorcock and Poul Anderson. [4] [5]The original version of D&D (1974) allowed players to choose among three alignments when creating a character: lawful, implying honor and respect for society's rules; chaotic, implying rebelliousness and individualism; and neutral, seeking a balance ...
For example, if A is a 3-by-0 matrix and B is a 0-by-3 matrix, then AB is the 3-by-3 zero matrix corresponding to the null map from a 3-dimensional space V to itself, while BA is a 0-by-0 matrix. There is no common notation for empty matrices, but most computer algebra systems allow creating and computing with them.
Destiny sold 91,277 physical retail copies for PlayStation 4 and 49,503 retail copies for PlayStation 3 within the first week of release in Japan, placing second and third place respectively within the Japanese software sales charts for that particular week. [190] Destiny was the third best-selling retail game in the United States in 2014. [191]
The determinant of a matrix A is commonly denoted det(A), det A, or | A |. Its value characterizes some properties of the matrix and the linear map represented, on a given basis, by the matrix. In particular, the determinant is nonzero if and only if the matrix is invertible and the corresponding linear map is an isomorphism.
The combat system was modified. The minimum number required to hit a target uses a mathematical formula in which the defender's armor class (AC) is subtracted from the attacker's THAC0 ("To Hit Armor Class '0 '") number, a simplification of 1st edition's attack matrix tables that had appeared as an optional rule in the 1st edition DMG ...
Changes of coordinates between different charts of the same region are required to be smooth. Just as contour lines on real-life maps encode changes in elevation, taking into account local distortions of the Earth's surface to calculate true distances, so the Riemannian metric describes distances and areas "in the small" in each local chart.