Parenthesis vs brackets for matrices - next
$begingroup$
I have read Parenthesis vs brackets for matrices
and I currently use brackets matrices (quaternions in 3D computing, in fact).
But I still have a doubt about the strict compatibility of notations between brackets and parenthesis, as explained in the previous topic.
I do think brackets are orientation dependent where parenthesis are not, which goes with comas usage… It's my question
$$
begin{pmatrix} 1, 2, 3, 6 end{pmatrix}
·
begin{pmatrix} 0, 1, 0, 0 end{pmatrix}
=
begin{pmatrix} -2, 1, 6, -3end{pmatrix}
$$
but
$$
begin{bmatrix}
1 \
2 \
3 \
6
end{bmatrix}
·
begin{bmatrix}
0 \
1 \
0 \
0
end{bmatrix}
=
begin{bmatrix}
-2\
1\
6\
-3
end{bmatrix}
$$
What's the truth ?
matrices
asked Mar 24 '17 at 10:32
SandburgSandburg
62
$endgroup$
add a comment |
$begingroup$
I have read Parenthesis vs brackets for matrices
and I currently use brackets matrices (quaternions in 3D computing, in fact).
But I still have a doubt about the strict compatibility of notations between brackets and parenthesis, as explained in the previous topic.
I do think brackets are orientation dependent where parenthesis are not, which goes with comas usage… It's my question
$$
begin{pmatrix} 1, 2, 3, 6 end{pmatrix}
·
begin{pmatrix} 0, 1, 0, 0 end{pmatrix}
=
begin{pmatrix} -2, 1, 6, -3end{pmatrix}
$$
but
$$
begin{bmatrix}
1 \
2 \
3 \
6
end{bmatrix}
·
begin{bmatrix}
0 \
1 \
0 \
0
end{bmatrix}
=
begin{bmatrix}
-2\
1\
6\
-3
end{bmatrix}
$$
What's the truth ?
matrices
asked Mar 24 '17 at 10:32
SandburgSandburg
62
$endgroup$
add a comment |
$begingroup$
I have read Parenthesis vs brackets for matrices
and I currently use brackets matrices (quaternions in 3D computing, in fact).
But I still have a doubt about the strict compatibility of notations between brackets and parenthesis, as explained in the previous topic.
I do think brackets are orientation dependent where parenthesis are not, which goes with comas usage… It's my question
$$
begin{pmatrix} 1, 2, 3, 6 end{pmatrix}
·
begin{pmatrix} 0, 1, 0, 0 end{pmatrix}
=
begin{pmatrix} -2, 1, 6, -3end{pmatrix}
$$
but
$$
begin{bmatrix}
1 \
2 \
3 \
6
end{bmatrix}
·
begin{bmatrix}
0 \
1 \
0 \
0
end{bmatrix}
=
begin{bmatrix}
-2\
1\
6\
-3
end{bmatrix}
$$
What's the truth ?
matrices
asked Mar 24 '17 at 10:32
SandburgSandburg
62
$endgroup$
I have read Parenthesis vs brackets for matrices
and I currently use brackets matrices (quaternions in 3D computing, in fact).
But I still have a doubt about the strict compatibility of notations between brackets and parenthesis, as explained in the previous topic.
I do think brackets are orientation dependent where parenthesis are not, which goes with comas usage… It's my question
$$
begin{pmatrix} 1, 2, 3, 6 end{pmatrix}
·
begin{pmatrix} 0, 1, 0, 0 end{pmatrix}
=
begin{pmatrix} -2, 1, 6, -3end{pmatrix}
$$
but
$$
begin{bmatrix}
1 \
2 \
3 \
6
end{bmatrix}
·
begin{bmatrix}
0 \
1 \
0 \
0
end{bmatrix}
=
begin{bmatrix}
-2\
1\
6\
-3
end{bmatrix}
$$
What's the truth ?
matrices
matrices
asked Mar 24 '17 at 10:32
SandburgSandburg
62
asked Mar 24 '17 at 10:32
SandburgSandburg
62
asked Mar 24 '17 at 10:32
SandburgSandburg
62
asked Mar 24 '17 at 10:32
SandburgSandburg
62
asked Mar 24 '17 at 10:32
SandburgSandburg
62
62
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Sometimes it is a matter of agreement. Many analysts use $(x_1,ldots,x_n)$ to denote vectors of $mathbb{R}^n$, while geometers and algebraists recommend
$$
begin{pmatrix}
x_1 \
vdots \
x_n
end{pmatrix}.
$$
Indeed analysts often confuse, in $mathbb{R}^n$, vectors and co-vectors (i.e. linear forms acting on vectors).
answered Mar 24 '17 at 10:38
SiminoreSiminore
30.6k33569
$endgroup$
add a comment |
$begingroup$
When you are working with only vectors in $Bbb R^n$, then it is convenient (from the type-setting point of view) to put the coordinates in a row and separate them by commas as a simple list of data like
$$
(1+epsilon,-1,x+y+z).
$$
Here parentheses are the most common (I guess because they are the most common delimiters), but it would be also acceptable to write
$$
[1+epsilon,-1,x+y+z],
$$
everybody would understand.
However, if you are working with vectors in matrix context then it becomes important to distinguish between rows and columns (I guess that's what you mean by orientation). Here there are no commas used, and the column notation for vectors is preferable (because then one can write "matrix times vector" as $Ax$). It is often used the same parenthesis delimiters like
$$
left(begin{matrix}1+epsilon & 1 & frac{pi}{2}\-1 & 43 & 87\ 1 & 1 & 1end{matrix}right)left(begin{matrix}1+epsilon\-1\x+y+zend{matrix}right)
$$
but if the vector/matrix becomes taller some people think that it is too much empty space between. One may flatten them out as LaTeX does, for example, but then the parentheses look pretty much similar to brackets, and, in this case, the brackets may look aesthetically preferable (especially with hand-writing on the blackboard).
$$
left(begin{matrix}1+epsilon\-1\12\21\32\43\54\65\x+y+zend{matrix}right),quad left[begin{matrix}1+epsilon\-1\12\21\32\43\54\65\x+y+zend{matrix}right]
$$
I do not think it is more than that in using different delimiters.
answered Mar 24 '17 at 11:06
A.Γ.A.Γ.
22.9k32656
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Sometimes it is a matter of agreement. Many analysts use $(x_1,ldots,x_n)$ to denote vectors of $mathbb{R}^n$, while geometers and algebraists recommend
$$
begin{pmatrix}
x_1 \
vdots \
x_n
end{pmatrix}.
$$
Indeed analysts often confuse, in $mathbb{R}^n$, vectors and co-vectors (i.e. linear forms acting on vectors).
answered Mar 24 '17 at 10:38
SiminoreSiminore
30.6k33569
$endgroup$
add a comment |
$begingroup$
Sometimes it is a matter of agreement. Many analysts use $(x_1,ldots,x_n)$ to denote vectors of $mathbb{R}^n$, while geometers and algebraists recommend
$$
begin{pmatrix}
x_1 \
vdots \
x_n
end{pmatrix}.
$$
Indeed analysts often confuse, in $mathbb{R}^n$, vectors and co-vectors (i.e. linear forms acting on vectors).
answered Mar 24 '17 at 10:38
SiminoreSiminore
30.6k33569
$endgroup$
add a comment |
$begingroup$
Sometimes it is a matter of agreement. Many analysts use $(x_1,ldots,x_n)$ to denote vectors of $mathbb{R}^n$, while geometers and algebraists recommend
$$
begin{pmatrix}
x_1 \
vdots \
x_n
end{pmatrix}.
$$
Indeed analysts often confuse, in $mathbb{R}^n$, vectors and co-vectors (i.e. linear forms acting on vectors).
answered Mar 24 '17 at 10:38
SiminoreSiminore
30.6k33569
$endgroup$
Sometimes it is a matter of agreement. Many analysts use $(x_1,ldots,x_n)$ to denote vectors of $mathbb{R}^n$, while geometers and algebraists recommend
$$
begin{pmatrix}
x_1 \
vdots \
x_n
end{pmatrix}.
$$
Indeed analysts often confuse, in $mathbb{R}^n$, vectors and co-vectors (i.e. linear forms acting on vectors).
answered Mar 24 '17 at 10:38
SiminoreSiminore
30.6k33569
answered Mar 24 '17 at 10:38
SiminoreSiminore
30.6k33569
answered Mar 24 '17 at 10:38
SiminoreSiminore
30.6k33569
answered Mar 24 '17 at 10:38
SiminoreSiminore
30.6k33569
30.6k33569
add a comment |
add a comment |
$begingroup$
When you are working with only vectors in $Bbb R^n$, then it is convenient (from the type-setting point of view) to put the coordinates in a row and separate them by commas as a simple list of data like
$$
(1+epsilon,-1,x+y+z).
$$
Here parentheses are the most common (I guess because they are the most common delimiters), but it would be also acceptable to write
$$
[1+epsilon,-1,x+y+z],
$$
everybody would understand.
However, if you are working with vectors in matrix context then it becomes important to distinguish between rows and columns (I guess that's what you mean by orientation). Here there are no commas used, and the column notation for vectors is preferable (because then one can write "matrix times vector" as $Ax$). It is often used the same parenthesis delimiters like
$$
left(begin{matrix}1+epsilon & 1 & frac{pi}{2}\-1 & 43 & 87\ 1 & 1 & 1end{matrix}right)left(begin{matrix}1+epsilon\-1\x+y+zend{matrix}right)
$$
but if the vector/matrix becomes taller some people think that it is too much empty space between. One may flatten them out as LaTeX does, for example, but then the parentheses look pretty much similar to brackets, and, in this case, the brackets may look aesthetically preferable (especially with hand-writing on the blackboard).
$$
left(begin{matrix}1+epsilon\-1\12\21\32\43\54\65\x+y+zend{matrix}right),quad left[begin{matrix}1+epsilon\-1\12\21\32\43\54\65\x+y+zend{matrix}right]
$$
I do not think it is more than that in using different delimiters.
answered Mar 24 '17 at 11:06
A.Γ.A.Γ.
22.9k32656
$endgroup$
add a comment |
$begingroup$
When you are working with only vectors in $Bbb R^n$, then it is convenient (from the type-setting point of view) to put the coordinates in a row and separate them by commas as a simple list of data like
$$
(1+epsilon,-1,x+y+z).
$$
Here parentheses are the most common (I guess because they are the most common delimiters), but it would be also acceptable to write
$$
[1+epsilon,-1,x+y+z],
$$
everybody would understand.
However, if you are working with vectors in matrix context then it becomes important to distinguish between rows and columns (I guess that's what you mean by orientation). Here there are no commas used, and the column notation for vectors is preferable (because then one can write "matrix times vector" as $Ax$). It is often used the same parenthesis delimiters like
$$
left(begin{matrix}1+epsilon & 1 & frac{pi}{2}\-1 & 43 & 87\ 1 & 1 & 1end{matrix}right)left(begin{matrix}1+epsilon\-1\x+y+zend{matrix}right)
$$
but if the vector/matrix becomes taller some people think that it is too much empty space between. One may flatten them out as LaTeX does, for example, but then the parentheses look pretty much similar to brackets, and, in this case, the brackets may look aesthetically preferable (especially with hand-writing on the blackboard).
$$
left(begin{matrix}1+epsilon\-1\12\21\32\43\54\65\x+y+zend{matrix}right),quad left[begin{matrix}1+epsilon\-1\12\21\32\43\54\65\x+y+zend{matrix}right]
$$
I do not think it is more than that in using different delimiters.
answered Mar 24 '17 at 11:06
A.Γ.A.Γ.
22.9k32656
$endgroup$
add a comment |
$begingroup$
When you are working with only vectors in $Bbb R^n$, then it is convenient (from the type-setting point of view) to put the coordinates in a row and separate them by commas as a simple list of data like
$$
(1+epsilon,-1,x+y+z).
$$
Here parentheses are the most common (I guess because they are the most common delimiters), but it would be also acceptable to write
$$
[1+epsilon,-1,x+y+z],
$$
everybody would understand.
However, if you are working with vectors in matrix context then it becomes important to distinguish between rows and columns (I guess that's what you mean by orientation). Here there are no commas used, and the column notation for vectors is preferable (because then one can write "matrix times vector" as $Ax$). It is often used the same parenthesis delimiters like
$$
left(begin{matrix}1+epsilon & 1 & frac{pi}{2}\-1 & 43 & 87\ 1 & 1 & 1end{matrix}right)left(begin{matrix}1+epsilon\-1\x+y+zend{matrix}right)
$$
but if the vector/matrix becomes taller some people think that it is too much empty space between. One may flatten them out as LaTeX does, for example, but then the parentheses look pretty much similar to brackets, and, in this case, the brackets may look aesthetically preferable (especially with hand-writing on the blackboard).
$$
left(begin{matrix}1+epsilon\-1\12\21\32\43\54\65\x+y+zend{matrix}right),quad left[begin{matrix}1+epsilon\-1\12\21\32\43\54\65\x+y+zend{matrix}right]
$$
I do not think it is more than that in using different delimiters.
answered Mar 24 '17 at 11:06
A.Γ.A.Γ.
22.9k32656
$endgroup$
When you are working with only vectors in $Bbb R^n$, then it is convenient (from the type-setting point of view) to put the coordinates in a row and separate them by commas as a simple list of data like
$$
(1+epsilon,-1,x+y+z).
$$
Here parentheses are the most common (I guess because they are the most common delimiters), but it would be also acceptable to write
$$
[1+epsilon,-1,x+y+z],
$$
everybody would understand.
However, if you are working with vectors in matrix context then it becomes important to distinguish between rows and columns (I guess that's what you mean by orientation). Here there are no commas used, and the column notation for vectors is preferable (because then one can write "matrix times vector" as $Ax$). It is often used the same parenthesis delimiters like
$$
left(begin{matrix}1+epsilon & 1 & frac{pi}{2}\-1 & 43 & 87\ 1 & 1 & 1end{matrix}right)left(begin{matrix}1+epsilon\-1\x+y+zend{matrix}right)
$$
but if the vector/matrix becomes taller some people think that it is too much empty space between. One may flatten them out as LaTeX does, for example, but then the parentheses look pretty much similar to brackets, and, in this case, the brackets may look aesthetically preferable (especially with hand-writing on the blackboard).
$$
left(begin{matrix}1+epsilon\-1\12\21\32\43\54\65\x+y+zend{matrix}right),quad left[begin{matrix}1+epsilon\-1\12\21\32\43\54\65\x+y+zend{matrix}right]
$$
I do not think it is more than that in using different delimiters.
answered Mar 24 '17 at 11:06
A.Γ.A.Γ.
22.9k32656
edited Mar 24 '17 at 13:01
answered Mar 24 '17 at 11:06
A.Γ.A.Γ.
22.9k32656
answered Mar 24 '17 at 11:06
A.Γ.A.Γ.
22.9k32656
answered Mar 24 '17 at 11:06
A.Γ.A.Γ.
22.9k32656
22.9k32656
add a comment |
add a comment |
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