An elementary matrix is an 
matrix obtained from the
identity
matrix 
by a single elementary row or column
operation.
An elementary matrix representing an elementary row operation is also called an elementary Gauss-Jordan
matrix (Achar 2000, p. 2). Matrix multiplication
on the left by this matrix performs the corresponding
elementary row operation on
another matrix.
See also
Elementary Row and Column Operations,
Gauss-Jordan Matrix,
Identity Matrix,
Matrix
Multiplication,
Permutation Matrix,
Shear Matrix
Portions of this entry contributed by Christopher
Stover
Explore with Wolfram|Alpha
References
Achar, P. N. "18.024-ESG Notes 2." p. 2, Spring 2000. https://www.math.lsu.edu/~pramod/tc/00s-024/no2.pdf.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, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, 1971.Referenced
on Wolfram|Alpha
Elementary Matrix
Cite this as:
Weisstein, Eric W., with contributions by Christopher Stover. "Elementary Matrix." From MathWorld--A
Wolfram Resource. https://mathworld.wolfram.com/ElementaryMatrix.html
Subject classifications
