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  2. Transpose - Wikipedia

    en.wikipedia.org/wiki/Transpose

    Ideally, one might hope to transpose a matrix with minimal additional storage. This leads to the problem of transposing an n × m matrix in-place, with O(1) additional storage or at most storage much less than mn. For n ≠ m, this involves a complicated permutation of the data elements that is non-trivial to implement in-place.

  3. In-place matrix transposition - Wikipedia

    en.wikipedia.org/wiki/In-place_matrix_transposition

    In-place matrix transposition, also called in-situ matrix transposition, is the problem of transposing an N×M matrix in-place in computer memory, ideally with O (bounded) additional storage, or at most with additional storage much less than NM.

  4. Contraposition - Wikipedia

    en.wikipedia.org/wiki/Contraposition

    In logic and mathematics, contraposition, or transposition, refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated proof method known as § Proof by contrapositive. The contrapositive of a statement has its antecedent and consequent inverted and flipped.

  5. 10 Hard Math Problems That Even the Smartest People in the ...

    www.aol.com/10-hard-math-problems-even-150000090...

    When we recently wrote about the toughest math problems that have been solved, we mentioned one of the greatest achievements in 20th-century math: the solution to Fermat’s Last Theorem. Sir ...

  6. Transposition - Wikipedia

    en.wikipedia.org/wiki/Transposition

    Transposition (mathematics), a permutation which exchanges two elements and keeps all others fixed; Transposition, producing the transpose of a matrix A T, which is computed by swapping columns for rows in the matrix A; Transpose of a linear map; Transposition (logic), a rule of replacement in philosophical logic

  7. Rule of replacement - Wikipedia

    en.wikipedia.org/wiki/Rule_of_replacement

    In logic, a rule of replacement [1] [2] [3] is a transformation rule that may be applied to only a particular segment of an expression.A logical system may be constructed so that it uses either axioms, rules of inference, or both as transformation rules for logical expressions in the system.

  8. Symmetric group - Wikipedia

    en.wikipedia.org/wiki/Symmetric_group

    A transposition is a permutation which exchanges two elements and keeps all others fixed; for example (1 3) is a transposition. Every permutation can be written as a product of transpositions; for instance, the permutation g from above can be written as g = (1 2)(2 5)(3 4).

  9. Transpositions matrix - Wikipedia

    en.wikipedia.org/wiki/Transpositions_matrix

    In example if , and , are two arbitrary selected elements from the same column q of matrix, then, matrix consists one fours of elements (,,,,,), for which are satisfied the equations , =, and , =,. This property, named “Tr-property” is specific to T r {\displaystyle Tr} matrices.

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