Content deleted Content added
KarlJacobi (talk | contribs) →Maximal rank: Schubert cells: Corrected limit of summation k => n. |
→Transformation to row echelon form: Fixed grammar Tags: canned edit summary Mobile edit Mobile app edit Android app edit |
||
Line 68:
\end{array} \right]</math>
For a matrix with [[integer]] coefficients, the [[Hermite normal form]] is a row echelon form that can be calculated without introducing any denominator, by using [[Euclidean division]] or [[Bézout's identity]]. The reduced echelon form of a matrix with integer coefficients generally contains non-integer coefficients, because of the need of dividing by its leading coefficient each row of
The non-uniqueness of the row echelon form of a matrix follows from the fact that some elementary row operations transform a matrix in row echelon form into another ([[row equivalence|equivalent]]) matrix that is also in row echelon form. These elementary row operations include the multiplication of a row by a nonzero scalar and the addition of a scalar multiple of a row to one of the above rows. For example:
| |||