Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a symplectic vector space is a vector space V equipped with a nondegenerate, skew-symmetric, bilinear form called the symplectic form.Working in a fixed basis, can be represented by a matrix. The two conditions above say that this matrix must be skew-symmetric and nonsingular. This is not the same thing as a symplectic matrix, which represents a...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a symplectic vector space is a vector space V equipped with a nondegenerate, skew-symmetric, bilinear form called the symplectic form.Working in a fixed basis, can be represented by a matrix. The two conditions above say that this matrix must be skew-symmetric and nonsingular. This is not the same thing as a symplectic matrix, which represents a symplectic transformation of the space.If V is finite-dimensional then its dimension must necessarily be even since every skew-symmetric matrix of odd size has determinant zero. A nondegenerate skew-symmetric bilinear form behaves quite differently from a nondegenerate symmetric bilinear form, such as the dot product on Euclidean vector spaces. With a Euclidean inner product g, we have g(v,v) > 0 for all nonzero vectors v, whereas a symplectic form satisfies (v,v) = 0.
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Пользователи привыкли почти мгновенно получать релевантные результаты от поисковых приложений. Чтобы создавать такие приложения, вы должны овладеть механизмами поиска. Однако для многих разработчиков тема ранжирования релевантности остается почти мистической. Данная книга срывает покров тайны с этой темы и демонстрирует, что механизм поиска - это всего лишь программируемый движок. На примере...
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