To divide something into two parts, interpret something as having two opposing aspects, or convert something into a pair.
From dual (adjective/noun) + -ize (a productive English suffix meaning 'to make or become'). The -ize suffix came through French from Late Latin -izare, originally from Greek.
In mathematics, dualizing is a powerful technique where you flip a geometry inside-out—flip points to planes and lines to lines—and sometimes the answer to a hard problem becomes obvious in the dual version.
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