An 
matrix 
is an elementary matrix if it differs from the 
identity 
by a single elementary
row or column operation.
Elementary Matrix
See also
Elementary Row and Column Operations, Identity Matrix, Permutation Matrix, Shear MatrixThis entry contributed by Christopher Stover
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References
Ayres, F. Jr. Schaum's Outline of Theory and Problems of Matrices. New York: Schaum, p. 41, 1962.Hoffman, K. and Kunze, R. Linear Algebra. Pearson, 1971.Cite this as:
Stover, Christopher. "Elementary Matrix." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ElementaryMatrix.html