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Diagonalization
The term
diagonalization
is used in two different senses in
mathematics
:
The process of finding a
diagonal matrix
similar to a given
square matrix
or representing a given
linear map
. See
diagonalizable
for more details.
A certain proof technique used to show that one
set
is larger than another. Examples are
Cantor's diagonal argument
to show that the set of
real numbers
is
uncountable
, the proof of Gödel's incompleteness theorem, and
Turing
's proof that no
algorithm
can solve the
halting problem
.