In logic and mathematics, diagonalization may refer to:
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Matrix diagonalization
In linear algebra, a square matrix A is called diagonalizable or non-defective if it is similar to a diagonal matrix. That is, if there exists an invertible matrix P and a diagonal matrix D such that . This is equivalent to (Such D are not ...
, a construction of a diagonal matrix (with nonzero entries only on the main diagonal) that is similar to a given matrix
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Diagonal argument (disambiguation) Diagonal argument can refer to:
* Diagonal argument (proof technique), proof techniques used in mathematics.
A diagonal argument, in mathematics, is a technique employed in the proofs of the following theorems:
*Cantor's diagonal argument (the ea ...
, various closely related proof techniques, including:
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Cantor's diagonal argument
Cantor's diagonal argument (among various similar namesthe diagonalisation argument, the diagonal slash argument, the anti-diagonal argument, the diagonal method, and Cantor's diagonalization proof) is a mathematical proof that there are infin ...
, used to prove that the set of real numbers is not countable
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Diagonal lemma
In mathematical logic, the diagonal lemma (also known as diagonalization lemma, self-reference lemma or fixed point theorem) establishes the existence of self-referential sentences in certain formal theories.
A particular instance of the diagonal ...
, used to create self-referential sentences in formal logic
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Table diagonalization
Diagonalization is the process of re-ordering the rows and columns of tables and charts so that the data forms an approximately diagonal line.Jacques Bertin, '' Semiology of Graphics: Diagrams, Networks, Maps''. ESRI Press, 2010, 168-169. This m ...
, a form of
data reduction Data reduction is the transformation of numerical or alphabetical digital information derived empirically or experimentally into a corrected, ordered, and simplified form. The purpose of data reduction can be two-fold: reduce the number of data rec ...
used to make interpretation of tables and charts easier.
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