Reduced row echelon form: Difference between revisions
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{{task|Matrices}}Show how to compute the '''reduced row echelon form''' (a.k.a. '''row canonical form''') of a matrix. The matrix can be stored in any datatype that is convenient (for most languages, this will probably be a two-dimensional array). |
{{wikipedia|Rref#Pseudocode}}{{task|Matrices}}Show how to compute the '''reduced row echelon form''' (a.k.a. '''row canonical form''') of a matrix. The matrix can be stored in any datatype that is convenient (for most languages, this will probably be a two-dimensional array). Built-in functions or this pseudocode (from Wikipedia) may be used: |
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'''function''' ToReducedRowEchelonForm(Matrix M) '''is''' |
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''lead'' := 0 |
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''rowCount'' := the number of rows in M |
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''columnCount'' := the number of columns in M |
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'''for''' 0 ≤ ''r'' < ''rowCount'' '''do''' |
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'''if''' ''columnCount'' ≤ ''lead'' '''then''' |
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'''stop''' |
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'''end if''' |
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''i'' = ''r'' |
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'''while''' M[''i'', ''lead''] = 0 '''do''' |
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''i'' = ''i'' + 1 |
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'''if''' ''rowCount'' = ''i'' '''then''' |
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''i'' = ''r'' |
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''lead'' = ''lead'' + 1 |
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'''if''' ''columnCount'' = ''lead'' '''then''' |
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'''stop''' |
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'''end if''' |
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'''end if''' |
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'''end while''' |
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Swap rows ''i'' and ''r'' |
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Divide row ''r'' by M[''r'', ''lead''] |
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'''for''' 0 ≤ ''i'' < ''rowCount'' '''do''' |
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'''if''' ''i'' ≠ ''r'' '''do''' |
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Subtract M[i, lead] multiplied by row ''r'' from row ''i'' |
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'''end if''' |
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'''end for''' |
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''lead'' = ''lead'' + 1 |
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'''end for''' |
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'''end function''' |
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For testing purposes, the RREF of this matrix: |
For testing purposes, the RREF of this matrix: |
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