Echelon Form -- From Wolfram MathWorld

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More...Less... Echelon Form

A matrix that has undergone Gaussian elimination is said to be in row echelon form or, more properly, "reduced echelon form" or "row-reduced echelon form." Such a matrix has the following characteristics:

1. All zero rows are at the bottom of the matrix

2. The leading entry of each nonzero row after the first occurs to the right of the leading entry of the previous row.

3. The leading entry in any nonzero row is 1.

4. All entries in the column above and below a leading 1 are zero.

Another common definition of echelon form only requires zeros below the leading ones, while the above definition also requires them above the leading ones.

See also

Gaussian Elimination

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More things to try:

  • conjugate transpose
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  • solve row echelon form {{1,2,4,5},{1,3,9,2},{1,4,16,5}}

References

Nakos, G. and Joyner, D. Linear Algebra with Applications. Pacific Grove, CA: Brooks/Cole, pp. 15-17, 1998.

Referenced on Wolfram|Alpha

Echelon Form

Cite this as:

Weisstein, Eric W. "Echelon Form." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/EchelonForm.html

Subject classifications

  • Algebra
  • Linear Algebra
  • Matrices
  • Matrix Operations
  • Algebra
  • Linear Algebra
  • Matrices
  • Matrix Types
  • MathWorld Contributors
  • Derwent
  • MathWorld Contributors
  • Pegg
More...Less... Created, developed and nurtured by Eric Weisstein at Wolfram Research

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