Canonical form

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In mathematics and computer science the term Canonical form, or sometimes Normal form refers to the usual representation of a mathematical object. For example, the canonical form of a positive integer in decimal representation is a finite sequence of digits that does not begin with zero.

Mathematics has defined equivalence relations for some objects. These equivalence realtions say that certain classes of objects are "equal". These objects then belong to the same equivalence class. In such a case, a canonical form consists in the choice of a specific object in each class. For example, row echelon form and Jordan normal form are canonical forms for matrices.