Math 2.0

Linear and multilinear algebra; matrix theory Theorem

Uniqueness of the reduced row echelon form

Builds on Reduced row echelon formRow equivalence

Statement

Let AA be a matrix. Then there is exactly one matrix in reduced row echelon form that is row equivalent to AA.

Remarks

Existence comes from row reduction. The content of the result is that two different reduced row echelon matrices are never row equivalent to the same matrix. So the reduced row echelon form of AA is well defined, and two matrices are row equivalent exactly when they have the same one.

Reading path

To understand this page from the ground up, read these 5 pages in order. The foundations come first.

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Matrix, definition, no evidence levelMatrixdefinitionReduced row echelon form, concept, no evidence levelReduced row echelon f…conceptElementary row operations, definition, no evidence levelElementary row operat…definitionRow equivalence, definition, no evidence levelRow equivalencedefinitionUniqueness of the reduced row echelon form, statement, no evidence levelUniqueness of the red…statement
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Matrix definition
  2. Reduced row echelon form concept
  3. Elementary row operations definition
  4. Row equivalence definition
  5. Uniqueness of the reduced row echelon form statement

Further reading

  1. Web https://github.com/davidaustinm/ula/blob/b6ea263ef23703072b7007485bb7a2d89c5f399b/src/section1-2.xml#L1343, src/section1-2.xml:1343
About this page
TagBF9SMZMJZE
URIm2://BF9SMZMJZE
Kindstatement, theorem
WritingW0 stub
MSC15A06
StatusThis copy of the site has no build data. Run m2 status BF9SMZMJZE.
AboutReduced row echelon form
UsesReduced row echelon form, Row equivalence
Changed4 November 2026

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