Math 2.0

Linear and multilinear algebra; matrix theory Definition

Row equivalence

Builds on Elementary row operations

Definition

Let FF be a field and let AA and BB be m×nm \times n matrices over FF. The matrix AA is row equivalent to BB when there is a finite sequence of elementary row operations that changes AA into BB.

Remarks

Row equivalence is an equivalence relation, because each elementary row operation has an inverse operation. The matrices AA and BB are row equivalent if and only if B=PAB = PA for an invertible m×mm \times m matrix PP. Each matrix is row equivalent to exactly one matrix in reduced row echelon form. Row equivalent matrices have the same row space and the same null space.

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To understand this page from the ground up, read these 3 pages in order. The foundations come first.

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Matrix, definition, no evidence levelMatrixdefinitionElementary row operations, definition, no evidence levelElementary row operat…definitionRow equivalence, definition, no evidence levelRow equivalencedefinition
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  1. Matrix definition
  2. Elementary row operations definition
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Further reading

  1. Web https://en.wikipedia.org/wiki/Row_equivalence, lead section
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