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The Taj Mahal complex can be conveniently divided into five sections: The 'moonlight garden' Mehtab Bagh to the north of the river Yamuna. The riverfront terrace, containing the Mausoleum, Mosque and Guest House. The Charbagh Garden containing pavilions. The western Naubat Khana is converted into a museum. The jilaukhana forecourt containing accommodation for the tomb attendants and two subsidiary tombs. The Taj Ganji, originally a bazaar and caravanserai only traces of which are still preserved. The great gate lies between the jilaukhana and the garden. Formal Analysis: At Eternitys Gate.
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Definition[ edit Formal Analysis: At Eternitys Gate Although seemingly different, the various approaches to defining tensors describe the same geometric concept using different language and at different levels of abstraction. For example, tensors are defined and discussed for statistical and machine learning applications. Just as a vector in an n- dimensional space is represented by a one-dimensional array with n components with respect to a given basisany tensor with respect to a basis is represented by a multidimensional array. The numbers in the multidimensional array are known as the scalar components of the tensor or simply its components.
They are denoted by indices giving their position in the array, as subscripts and superscriptsfollowing the symbolic name of the tensor. For example, the components of an order 2 tensor T could be denoted Tijwhere i and j are indices running from 1 to n, or also by T i j.
Whether an index is displayed as a superscript or subscript depends on the transformation properties of the tensor, described below. Thus while Tij and T i j can both be expressed as n by n matrices, and are numerically related via index jugglingthe difference in their transformation laws indicates it would be improper to add them together. The total number of indices required to identify each component uniquely is equal to the dimension of the array, and is called the order, degree or rank of the tensor.
However, the term "rank" generally has another meaning in the context of matrices and Analyxis:. Just as the components of a vector change when we change the basis of the vector space, the components of a tensor also change under such a transformation. Each type of tensor comes equipped with a transformation law that details how the components of the tensor respond to a change of basis.
The components of a vector can respond in two distinct ways to a change of basis see covariance and contravariance of vectorswhere the new basis vectors e.]
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