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elementary matrix

The identity matrix after one elementary row operation; multiplying by it performs that operation.

An elementary matrix is any matrix obtained by applying exactly one elementary row operation to the identity I_n. For any matrix A with the right number of rows, EA is exactly A with that row operation applied — left multiplication by E performs the operation. Every elementary matrix is invertible, and its inverse is itself elementary.

See also

elementary row operations LU factorization
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