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  2. Hill cipher - Wikipedia

    en.wikipedia.org/wiki/Hill_cipher

    Hill's cipher machine, from figure 4 of the patent. In classical cryptography, the Hill cipher is a polygraphic substitution cipher based on linear algebra.Invented by Lester S. Hill in 1929, it was the first polygraphic cipher in which it was practical (though barely) to operate on more than three symbols at once.

  3. Overdetermined system - Wikipedia

    en.wikipedia.org/wiki/Overdetermined_system

    This case yields no solution. Example: x = 1, x = 2. M > N but only K equations (K < M and K ≤ N+1) are linearly independent. There exist three possible sub-cases of this: K = N+1. This case yields no solutions. Example: 2x = 2, x = 1, x = 2. K = N. This case yields either a single solution or no solution, the latter occurring when the ...

  4. System of linear equations - Wikipedia

    en.wikipedia.org/wiki/System_of_linear_equations

    In general, a system with fewer equations than unknowns has infinitely many solutions, but it may have no solution. Such a system is known as an underdetermined system. In general, a system with the same number of equations and unknowns has a single unique solution. In general, a system with more equations than unknowns has no solution.

  5. Underdetermined system - Wikipedia

    en.wikipedia.org/wiki/Underdetermined_system

    If, on the other hand, the ranks of these two matrices are equal, the system must have at least one solution; since in an underdetermined system this rank is necessarily less than the number of unknowns, there are indeed an infinitude of solutions, with the general solution having k free parameters where k is the difference between the number ...

  6. Tridiagonal matrix algorithm - Wikipedia

    en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm

    Indeed, multiplying each equation of the second auxiliary system by , adding with the corresponding equation of the first auxiliary system and using the representation = +, we immediately see that equations number 2 through n of the original system are satisfied; it only remains to satisfy equation number 1.

  7. System of polynomial equations - Wikipedia

    en.wikipedia.org/wiki/System_of_polynomial_equations

    For example, if a system contains , a system over the rational numbers is obtained by adding the equation r 2 22 = 0 and replacing by r 2 in the other equations. In the case of a finite field, the same transformation allows always supposing that the field k has a prime order.

  8. Unicity distance - Wikipedia

    en.wikipedia.org/wiki/Unicity_distance

    Now an alphabet of 32 characters can carry 5 bits of information per character (as 32 = 2 5). In general the number of bits of information per character is log 2 (N), where N is the number of characters in the alphabet and log 2 is the binary logarithm. So for English each character can convey log 2 (26) = 4.7 bits of information.

  9. Indeterminate system - Wikipedia

    en.wikipedia.org/wiki/Indeterminate_system

    An indeterminate system by definition is consistent, in the sense of having at least one solution. [3] For a system of linear equations, the number of equations in an indeterminate system could be the same as the number of unknowns, less than the number of unknowns (an underdetermined system), or greater than the number of unknowns (an ...

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