diagonalize

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diagonalize

[dī′ag·ən·ə‚līz]
(mathematics)
To convert a square matrix to a diagonal matrix, usually by multiplying it on the left by a second matrix A of the same order, and on the right by the inverse of A.
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Gamma]] as are the canonical representations of ordinal addition, the resources for diagonalisation and so forth.
39) Or of that hierarchy of G6delian proof predicates characterising ever stronger notions of proof which is generated by adding as an axiom at each stage [Alpha] the hitherto undecidable diagonalisation on "unprovably", [Beta] [is less than] [Alpha].
If t is any term, let its diagonalisation be the term obtained by substituting <t> for each free variable in t.
In this, [phi](x) is "x is a definable real number between 0 and 1", so that w is the set of such reals, DR; [psi](x) is "x is definable" and [delta](x) is diag(x), a real, defined by diagonalisation on x, in such a way as to ensure that [delta](x)[not an element of