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**HERMITE(***matrix***)**

where *matrix* is a numeric matrix or literal.

The HERMITE function uses elementary row operations to reduce a matrix to Hermite normal form. For square matrices this normal form is upper-triangular and idempotent.

If the argument is square and nonsingular, the result will be the identity matrix. In general the result satisfies the following four conditions (Graybill 1969, p. 120):

- It is upper-triangular.
- It has only values of 0 and 1 on the diagonal.
- If a row has a 0 on the diagonal, then every element in that row is 0.
- If a row has a 1 on the diagonal, then every off-diagonal element is 0 in the column in which the 1 appears.

a={3 6 9, 1 2 5, 2 4 10}; h=hermite(a);These statements produce

H 3 rows 3 cols (numeric) 1 2 0 0 0 0 0 0 1If the argument is a square matrix, then the Hermite normal form can be transformed into the row echelon form by rearranging rows in which all values are 0.

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