Contragredient meaning

(mathematics) Generally, an object contragredient to another is the object inversed and transposed.
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(mathematics) A contragredient representation in linear algebra is the transpose of the former representation of an inverse object.
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(mathematics) A contragredient matrix is a transpose of an inverse matrix.
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Origin of contragredient

  • Neologism based on the English prefix contra- and gredient. Gredient may be based on the English word grid, since the mathematical objects referred to as contragredient are often represented as grids of numbers.
    From Wiktionary

Contragredient Sentence Examples

  • For this reason the umbrae A1, A 2 are said to be contragredient to xi, x 2.

  • are said to be contragredient when the linear substitutions for the first set are x =A1X+u1Y-}-v1Z-?--..., y = A2X+,u2Y +v2Z �..., Z = A 3 X +�3Y -1v 3 Z - -..., and these are associated with the following formulae appertaining to the second set, .`"?.

  • are contragredient with the d- variables x, y, z, ...

  • If u, a quantic in x, y, z, ..., be expressed in terms of new variables X, Y, Z ...; and if, n,, ..., be quantities contragredient to x, y, z, ...; there are found to exist functions of, n, ?, ..., and of the coefficients in u, which need, at most, be multiplied by powers of the modulus to be made equal to the same functions of E, H, Z, ...

  • He proves, by means of the six linear partial differential equations satisfied by the concomitants, that, if any concomitant be expanded in powers of xi, x 2, x 3, the point variables-and of u 8, u 2, u3, the contragredient line variables-it is completely determinate if its leading coefficient be known.

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Words near contragredient in the Dictionary