Is there a reason vectors in space are represented as column vectors (in that nothing works with row...
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As opposed to row vectors? It would seem that whenever performing operations on vectors in space (applying a matrix/linear transformation to it, for example) does not work unless the vector is in it's column form (since lots of things, such as matrix multiplication, are dependent on dimensionality). Why is it that things work with column vectors but not row vectors?
linear-algebra vectors
asked Dec 15 '18 at 15:35
James RonaldJames Ronald
1007
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show 6 more comments
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As opposed to row vectors? It would seem that whenever performing operations on vectors in space (applying a matrix/linear transformation to it, for example) does not work unless the vector is in it's column form (since lots of things, such as matrix multiplication, are dependent on dimensionality). Why is it that things work with column vectors but not row vectors?
linear-algebra vectors
asked Dec 15 '18 at 15:35
James RonaldJames Ronald
1007
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Things do work just as well with row vectors.
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– Lord Shark the Unknown
Dec 15 '18 at 15:36
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Both of them work. Just the column one is easy to use as in notations.
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– xbh
Dec 15 '18 at 15:38
4
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If you write vectors as rows, then applying a linear transformation is achieved by multiplying by a matrix on the right: $y=xA$.
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– Rahul
Dec 15 '18 at 15:40
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Any asymmetry encountered in mathematics is due to human intervention and convention.
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– John L Winters
Dec 15 '18 at 15:52
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@John Strongly disagree. What about nonabelian groups, which are fundamentally asymmetric?
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– Matt Samuel
Dec 15 '18 at 15:55
|
show 6 more comments
$begingroup$
As opposed to row vectors? It would seem that whenever performing operations on vectors in space (applying a matrix/linear transformation to it, for example) does not work unless the vector is in it's column form (since lots of things, such as matrix multiplication, are dependent on dimensionality). Why is it that things work with column vectors but not row vectors?
linear-algebra vectors
asked Dec 15 '18 at 15:35
James RonaldJames Ronald
1007
$endgroup$
As opposed to row vectors? It would seem that whenever performing operations on vectors in space (applying a matrix/linear transformation to it, for example) does not work unless the vector is in it's column form (since lots of things, such as matrix multiplication, are dependent on dimensionality). Why is it that things work with column vectors but not row vectors?
linear-algebra vectors
linear-algebra vectors
asked Dec 15 '18 at 15:35
James RonaldJames Ronald
1007
asked Dec 15 '18 at 15:35
James RonaldJames Ronald
1007
asked Dec 15 '18 at 15:35
James RonaldJames Ronald
1007
asked Dec 15 '18 at 15:35
James RonaldJames Ronald
1007
asked Dec 15 '18 at 15:35
James RonaldJames Ronald
1007
1007
$begingroup$
Things do work just as well with row vectors.
$endgroup$
– Lord Shark the Unknown
Dec 15 '18 at 15:36
$begingroup$
Both of them work. Just the column one is easy to use as in notations.
$endgroup$
– xbh
Dec 15 '18 at 15:38
4
$begingroup$
If you write vectors as rows, then applying a linear transformation is achieved by multiplying by a matrix on the right: $y=xA$.
$endgroup$
– Rahul
Dec 15 '18 at 15:40
$begingroup$
Any asymmetry encountered in mathematics is due to human intervention and convention.
$endgroup$
– John L Winters
Dec 15 '18 at 15:52
$begingroup$
@John Strongly disagree. What about nonabelian groups, which are fundamentally asymmetric?
$endgroup$
– Matt Samuel
Dec 15 '18 at 15:55
|
show 6 more comments
$begingroup$
Things do work just as well with row vectors.
$endgroup$
– Lord Shark the Unknown
Dec 15 '18 at 15:36
$begingroup$
Both of them work. Just the column one is easy to use as in notations.
$endgroup$
– xbh
Dec 15 '18 at 15:38
4
$begingroup$
If you write vectors as rows, then applying a linear transformation is achieved by multiplying by a matrix on the right: $y=xA$.
$endgroup$
– Rahul
Dec 15 '18 at 15:40
$begingroup$
Any asymmetry encountered in mathematics is due to human intervention and convention.
$endgroup$
– John L Winters
Dec 15 '18 at 15:52
$begingroup$
@John Strongly disagree. What about nonabelian groups, which are fundamentally asymmetric?
$endgroup$
– Matt Samuel
Dec 15 '18 at 15:55
$begingroup$
Things do work just as well with row vectors.
$endgroup$
– Lord Shark the Unknown
Dec 15 '18 at 15:36
$begingroup$
Things do work just as well with row vectors.
$endgroup$
– Lord Shark the Unknown
Dec 15 '18 at 15:36
$begingroup$
Both of them work. Just the column one is easy to use as in notations.
$endgroup$
– xbh
Dec 15 '18 at 15:38
$begingroup$
Both of them work. Just the column one is easy to use as in notations.
$endgroup$
– xbh
Dec 15 '18 at 15:38
4
4
$begingroup$
If you write vectors as rows, then applying a linear transformation is achieved by multiplying by a matrix on the right: $y=xA$.
$endgroup$
– Rahul
Dec 15 '18 at 15:40
$begingroup$
If you write vectors as rows, then applying a linear transformation is achieved by multiplying by a matrix on the right: $y=xA$.
$endgroup$
– Rahul
Dec 15 '18 at 15:40
$begingroup$
Any asymmetry encountered in mathematics is due to human intervention and convention.
$endgroup$
– John L Winters
Dec 15 '18 at 15:52
$begingroup$
Any asymmetry encountered in mathematics is due to human intervention and convention.
$endgroup$
– John L Winters
Dec 15 '18 at 15:52
$begingroup$
@John Strongly disagree. What about nonabelian groups, which are fundamentally asymmetric?
$endgroup$
– Matt Samuel
Dec 15 '18 at 15:55
$begingroup$
@John Strongly disagree. What about nonabelian groups, which are fundamentally asymmetric?
$endgroup$
– Matt Samuel
Dec 15 '18 at 15:55
|
show 6 more comments
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$begingroup$
Things do work just as well with row vectors.
$endgroup$
– Lord Shark the Unknown
Dec 15 '18 at 15:36
$begingroup$
Both of them work. Just the column one is easy to use as in notations.
$endgroup$
– xbh
Dec 15 '18 at 15:38
4
$begingroup$
If you write vectors as rows, then applying a linear transformation is achieved by multiplying by a matrix on the right: $y=xA$.
$endgroup$
– Rahul
Dec 15 '18 at 15:40
$begingroup$
Any asymmetry encountered in mathematics is due to human intervention and convention.
$endgroup$
– John L Winters
Dec 15 '18 at 15:52
$begingroup$
@John Strongly disagree. What about nonabelian groups, which are fundamentally asymmetric?
$endgroup$
– Matt Samuel
Dec 15 '18 at 15:55