Proving two canonical forms with identical row spaces are identical
I've been trying to prove that any two matrices (of the same dimension) that generate the same row space are necessarily row equivalent as follows:
We can reduce each of the two matrices to its canonical form, which has the same row space as the original matrices. If I can say that the canonical forms are identical, then it is implied that the two matrices are row equivalent, but how can I deduce that the two canonical forms are in fact identical?
linear-algebra matrices
asked Dec 4 '18 at 11:00
Matan Haller
255
add a comment |
I've been trying to prove that any two matrices (of the same dimension) that generate the same row space are necessarily row equivalent as follows:
We can reduce each of the two matrices to its canonical form, which has the same row space as the original matrices. If I can say that the canonical forms are identical, then it is implied that the two matrices are row equivalent, but how can I deduce that the two canonical forms are in fact identical?
linear-algebra matrices
asked Dec 4 '18 at 11:00
Matan Haller
255
add a comment |
I've been trying to prove that any two matrices (of the same dimension) that generate the same row space are necessarily row equivalent as follows:
We can reduce each of the two matrices to its canonical form, which has the same row space as the original matrices. If I can say that the canonical forms are identical, then it is implied that the two matrices are row equivalent, but how can I deduce that the two canonical forms are in fact identical?
linear-algebra matrices
asked Dec 4 '18 at 11:00
Matan Haller
255
I've been trying to prove that any two matrices (of the same dimension) that generate the same row space are necessarily row equivalent as follows:
We can reduce each of the two matrices to its canonical form, which has the same row space as the original matrices. If I can say that the canonical forms are identical, then it is implied that the two matrices are row equivalent, but how can I deduce that the two canonical forms are in fact identical?
linear-algebra matrices
linear-algebra matrices
asked Dec 4 '18 at 11:00
Matan Haller
255
asked Dec 4 '18 at 11:00
Matan Haller
255
asked Dec 4 '18 at 11:00
Matan Haller
255
asked Dec 4 '18 at 11:00
Matan Haller
255
asked Dec 4 '18 at 11:00
Matan Haller
255
255
add a comment |
add a comment |
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