echelon form
"Echelon form" is a concept in linear algebra used to simplify matrices, making it easier to solve linear equations and analyze matrix properties.
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Definition
C1Linear Algebra
(technical, academic)A matrix arrangement where each leading entry in a row is to the right of the leading entry in the row above, and all rows of zeros are at the bottom.
Example
- The matrix was transformed into echelon form to simplify solving the system of equations.
C1Linear Algebra
(technical, academic)A specific matrix arrangement where each leading entry is 1, and each column containing a leading 1 has zeros in all other positions.
Example
- Converting a matrix to its reduced row echelon form can help in finding the inverse of the matrix.
Similar
Terms that have similar or relatively close meanings to "echelon form":
en echelonquadratic formmultilinear formclosed formrear echelonnormal form