parallelotope sentence in Hindi
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- It could be any shape, although the volume equals that of the parallelotope.
- Inversion in this point leaves the " n "-parallelotope unchanged.
- Geometrically, the Gram determinant is the square of the volume of the parallelotope formed by the vectors.
- More generally a parallelotope, or " voronoi parallelotope ", has parallel and congruent opposite facets.
- More generally a parallelotope, or " voronoi parallelotope ", has parallel and congruent opposite facets.
- The diagonals of an " n "-parallelotope intersect at one point and are bisected by this point.
- In the case " m " = 1 the parallelotope is reduced to a single vector and its volume its length.
- An " n "-vector doesn't necessarily have a shape of a parallelotope this is a convenient visualization.
- However, if one wishes to define a function that assigns a volume for any such parallelotope, it should satisfy the following properties:
- This formula expresses the fact that the absolute value of the determinant of a matrix equals the volume of the parallelotope spanned by its columns or rows.
- So a " 2 "-parallelotope is a parallelogon which can also include certain hexagons, and a " 3 "-parallelotope is a parallelohedron, including 5 types of polyhedra.
- So a " 2 "-parallelotope is a parallelogon which can also include certain hexagons, and a " 3 "-parallelotope is a parallelohedron, including 5 types of polyhedra.
- If a-form is thought of as measuring the flux through an infinitesimal-parallelotope, then its exterior derivative can be thought of as measuring the net flux through the boundary of a-parallelotope.
- If a-form is thought of as measuring the flux through an infinitesimal-parallelotope, then its exterior derivative can be thought of as measuring the net flux through the boundary of a-parallelotope.
- In general, there does not exist a natural concept of a " volume " for a parallelotope generated by vectors in a " n "-dimensional vector space " V ".
- From geometric algebra, we interpret the pseudoscalar e _ 1 \ wedge e _ 2 \ wedge \ cdots \ wedge e _ n to be the signed volume of the " n "-parallelotope subtended by these basis vectors.
- Similarly, the volume of any " n "-simplex that shares " n " converging edges of a parallelotope has a volume equal to one 1 / " n ! " of the volume of that parallelotope.
- Similarly, the volume of any " n "-simplex that shares " n " converging edges of a parallelotope has a volume equal to one 1 / " n ! " of the volume of that parallelotope.
- The edges radiating from one vertex of a " k "-parallelotope form a " k "-frame ( v _ 1, \ ldots, v _ n ) of the vector space, and the parallelotope can be recovered from these vectors, by taking linear combinations of the vectors, with weights between 0 and 1.
- The edges radiating from one vertex of a " k "-parallelotope form a " k "-frame ( v _ 1, \ ldots, v _ n ) of the vector space, and the parallelotope can be recovered from these vectors, by taking linear combinations of the vectors, with weights between 0 and 1.
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