Row equivalence
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Row equivalent is a term used to describe two matrices which can be transformed from one another using elementary row operations.
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[edit] Notation
While there is not an explicit notation to show which row operation was used, a tilde (~) between two matrices indicates that they are row-equivalent. The operation that was used can generally be deduced from the given matrices.
[edit] Meaning
In linear algebra, 2 row-equivalent augmented matrices describe the same system of linear equations. Row-equivalent matrices are often used to simplify calculations and reduce error.
[edit] Directionality
Because all elementary row operations are reversible using other elementary row operations, the order in which two row-equivalent matices are stated is insignificant. Equivalency is implied in both directions.
