Diagonalization
Encyclopedia
In mathematics, diagonalization may refer to:
- Diagonal matrixDiagonal matrixIn linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero. The diagonal entries themselves may or may not be zero...
, which is in a form with nonzero entries only on the main diagonal - Diagonalizable matrixDiagonalizable matrixIn linear algebra, a square matrix A is called diagonalizable if it is similar to a diagonal matrix, i.e., if there exists an invertible matrix P such that P −1AP is a diagonal matrix...
, which can be put into a form with nonzero entries only on the main diagonal - Diagonal lemmaDiagonal lemmaIn mathematical logic, the diagonal lemma or fixed point theorem establishes the existence of self-referential sentences in certain formal theories of the natural numbers -- specifically those theories that are strong enough to represent all computable functions...
, used to create self-referential sentences in formal logic - Diagonal argument (disambiguation), various
- Cantor's diagonal argumentCantor's diagonal argumentCantor's diagonal argument, also called the diagonalisation argument, the diagonal slash argument or the diagonal method, was published in 1891 by Georg Cantor as a mathematical proof that there are infinite sets which cannot be put into one-to-one correspondence with the infinite set of natural...
, used to prove that the set of real numbers is not countable