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In linear algebra and ring theory, the Howell normal form is a generalization of the row echelon form of a matrix over Z N {\displaystyle \mathbb {Z} _{N}} , the ring of integers modulo N. The row spans of two matrices agree if, and only if, their Howell normal forms agree. The Howell normal form generalizes the Hermite normal form, which is defined for matrices over Z {\displaystyle \mathbb {Z} }.
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