Transpose notation
$begingroup$
After using the transpose for a while, I wondered if there in any vague connection to other superscript stuff like exponents or something. I doubt it, but I couldn't find anything and it seems weird to have it as a superscript. Is there anything deeper going on here?
Question: Is there a reason for this notation? It's bothered me from since I learned it.
notation transpose
asked Jan 6 at 13:34
Benjamin ThoburnBenjamin Thoburn
317111
$endgroup$
add a comment |
$begingroup$
After using the transpose for a while, I wondered if there in any vague connection to other superscript stuff like exponents or something. I doubt it, but I couldn't find anything and it seems weird to have it as a superscript. Is there anything deeper going on here?
Question: Is there a reason for this notation? It's bothered me from since I learned it.
notation transpose
asked Jan 6 at 13:34
Benjamin ThoburnBenjamin Thoburn
317111
$endgroup$
$begingroup$
Where else could we put the $T$? $A_T$ looks in the context of matrices like the $T$th component of a vector. I suppose we could use ${}^TA$ or ${}_TA$, or dispense with $T$ altogether with notation such as $bar{A}$. Good luck keeping track of the difference between transposes and Hermitian adjoints of complex matrices then, though.
$endgroup$
– J.G.
Jan 6 at 17:05
$begingroup$
In fact some sources do use ${}^TA$. Other sources use a prime to indicate the transpose, with the obvious potential for confusion.
$endgroup$
– amd
Jan 6 at 21:08
$begingroup$
@J.G. What about T$(A)$
$endgroup$
– Benjamin Thoburn
Jan 6 at 21:37
add a comment |
$begingroup$
After using the transpose for a while, I wondered if there in any vague connection to other superscript stuff like exponents or something. I doubt it, but I couldn't find anything and it seems weird to have it as a superscript. Is there anything deeper going on here?
Question: Is there a reason for this notation? It's bothered me from since I learned it.
notation transpose
asked Jan 6 at 13:34
Benjamin ThoburnBenjamin Thoburn
317111
$endgroup$
After using the transpose for a while, I wondered if there in any vague connection to other superscript stuff like exponents or something. I doubt it, but I couldn't find anything and it seems weird to have it as a superscript. Is there anything deeper going on here?
Question: Is there a reason for this notation? It's bothered me from since I learned it.
notation transpose
notation transpose
asked Jan 6 at 13:34
Benjamin ThoburnBenjamin Thoburn
317111
asked Jan 6 at 13:34
Benjamin ThoburnBenjamin Thoburn
317111
asked Jan 6 at 13:34
Benjamin ThoburnBenjamin Thoburn
317111
asked Jan 6 at 13:34
Benjamin ThoburnBenjamin Thoburn
317111
asked Jan 6 at 13:34
Benjamin ThoburnBenjamin Thoburn
317111
317111
$begingroup$
Where else could we put the $T$? $A_T$ looks in the context of matrices like the $T$th component of a vector. I suppose we could use ${}^TA$ or ${}_TA$, or dispense with $T$ altogether with notation such as $bar{A}$. Good luck keeping track of the difference between transposes and Hermitian adjoints of complex matrices then, though.
$endgroup$
– J.G.
Jan 6 at 17:05
$begingroup$
In fact some sources do use ${}^TA$. Other sources use a prime to indicate the transpose, with the obvious potential for confusion.
$endgroup$
– amd
Jan 6 at 21:08
$begingroup$
@J.G. What about T$(A)$
$endgroup$
– Benjamin Thoburn
Jan 6 at 21:37
add a comment |
$begingroup$
Where else could we put the $T$? $A_T$ looks in the context of matrices like the $T$th component of a vector. I suppose we could use ${}^TA$ or ${}_TA$, or dispense with $T$ altogether with notation such as $bar{A}$. Good luck keeping track of the difference between transposes and Hermitian adjoints of complex matrices then, though.
$endgroup$
– J.G.
Jan 6 at 17:05
$begingroup$
In fact some sources do use ${}^TA$. Other sources use a prime to indicate the transpose, with the obvious potential for confusion.
$endgroup$
– amd
Jan 6 at 21:08
$begingroup$
@J.G. What about T$(A)$
$endgroup$
– Benjamin Thoburn
Jan 6 at 21:37
$begingroup$
Where else could we put the $T$? $A_T$ looks in the context of matrices like the $T$th component of a vector. I suppose we could use ${}^TA$ or ${}_TA$, or dispense with $T$ altogether with notation such as $bar{A}$. Good luck keeping track of the difference between transposes and Hermitian adjoints of complex matrices then, though.
$endgroup$
– J.G.
Jan 6 at 17:05
$begingroup$
Where else could we put the $T$? $A_T$ looks in the context of matrices like the $T$th component of a vector. I suppose we could use ${}^TA$ or ${}_TA$, or dispense with $T$ altogether with notation such as $bar{A}$. Good luck keeping track of the difference between transposes and Hermitian adjoints of complex matrices then, though.
$endgroup$
– J.G.
Jan 6 at 17:05
$begingroup$
In fact some sources do use ${}^TA$. Other sources use a prime to indicate the transpose, with the obvious potential for confusion.
$endgroup$
– amd
Jan 6 at 21:08
$begingroup$
In fact some sources do use ${}^TA$. Other sources use a prime to indicate the transpose, with the obvious potential for confusion.
$endgroup$
– amd
Jan 6 at 21:08
$begingroup$
@J.G. What about T$(A)$
$endgroup$
– Benjamin Thoburn
Jan 6 at 21:37
$begingroup$
@J.G. What about T$(A)$
$endgroup$
– Benjamin Thoburn
Jan 6 at 21:37
add a comment |
2 Answers
2
active
oldest
votes
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It's just the conventional notation and is used for the conjugate transpose too: $mathbf A^mathsf {H}$.
As the Wikipedia entry on the transpose of a matrix points out, you can use ${mathbf {A}}^{top}$ (top) instead of $mathbf {A}^{T}$ to make it stand out a bit better if that helps:
To avoid confusing the reader between the transpose operation and a matrix raised to the $mathbf A^{th}$ power, the $mathbf {A}^{top}$ symbol denotes the transpose operation.
answered Jan 6 at 17:25
EdOverflowEdOverflow
2059
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add a comment |
$begingroup$
If $A$ is a real orthogonal matrix, then
$$A^{-1} = A^T$$
This is the only little thing I can think of.
answered Jan 6 at 16:58
DamienDamien
58214
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add a comment |
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2 Answers
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active
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2 Answers
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active
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$begingroup$
It's just the conventional notation and is used for the conjugate transpose too: $mathbf A^mathsf {H}$.
As the Wikipedia entry on the transpose of a matrix points out, you can use ${mathbf {A}}^{top}$ (top) instead of $mathbf {A}^{T}$ to make it stand out a bit better if that helps:
To avoid confusing the reader between the transpose operation and a matrix raised to the $mathbf A^{th}$ power, the $mathbf {A}^{top}$ symbol denotes the transpose operation.
answered Jan 6 at 17:25
EdOverflowEdOverflow
2059
$endgroup$
add a comment |
$begingroup$
It's just the conventional notation and is used for the conjugate transpose too: $mathbf A^mathsf {H}$.
As the Wikipedia entry on the transpose of a matrix points out, you can use ${mathbf {A}}^{top}$ (top) instead of $mathbf {A}^{T}$ to make it stand out a bit better if that helps:
To avoid confusing the reader between the transpose operation and a matrix raised to the $mathbf A^{th}$ power, the $mathbf {A}^{top}$ symbol denotes the transpose operation.
answered Jan 6 at 17:25
EdOverflowEdOverflow
2059
$endgroup$
add a comment |
$begingroup$
It's just the conventional notation and is used for the conjugate transpose too: $mathbf A^mathsf {H}$.
As the Wikipedia entry on the transpose of a matrix points out, you can use ${mathbf {A}}^{top}$ (top) instead of $mathbf {A}^{T}$ to make it stand out a bit better if that helps:
To avoid confusing the reader between the transpose operation and a matrix raised to the $mathbf A^{th}$ power, the $mathbf {A}^{top}$ symbol denotes the transpose operation.
answered Jan 6 at 17:25
EdOverflowEdOverflow
2059
$endgroup$
It's just the conventional notation and is used for the conjugate transpose too: $mathbf A^mathsf {H}$.
As the Wikipedia entry on the transpose of a matrix points out, you can use ${mathbf {A}}^{top}$ (top) instead of $mathbf {A}^{T}$ to make it stand out a bit better if that helps:
To avoid confusing the reader between the transpose operation and a matrix raised to the $mathbf A^{th}$ power, the $mathbf {A}^{top}$ symbol denotes the transpose operation.
answered Jan 6 at 17:25
EdOverflowEdOverflow
2059
answered Jan 6 at 17:25
EdOverflowEdOverflow
2059
answered Jan 6 at 17:25
EdOverflowEdOverflow
2059
answered Jan 6 at 17:25
EdOverflowEdOverflow
2059
2059
add a comment |
add a comment |
$begingroup$
If $A$ is a real orthogonal matrix, then
$$A^{-1} = A^T$$
This is the only little thing I can think of.
answered Jan 6 at 16:58
DamienDamien
58214
$endgroup$
add a comment |
$begingroup$
If $A$ is a real orthogonal matrix, then
$$A^{-1} = A^T$$
This is the only little thing I can think of.
answered Jan 6 at 16:58
DamienDamien
58214
$endgroup$
add a comment |
$begingroup$
If $A$ is a real orthogonal matrix, then
$$A^{-1} = A^T$$
This is the only little thing I can think of.
answered Jan 6 at 16:58
DamienDamien
58214
$endgroup$
If $A$ is a real orthogonal matrix, then
$$A^{-1} = A^T$$
This is the only little thing I can think of.
answered Jan 6 at 16:58
DamienDamien
58214
answered Jan 6 at 16:58
DamienDamien
58214
answered Jan 6 at 16:58
DamienDamien
58214
answered Jan 6 at 16:58
DamienDamien
58214
58214
add a comment |
add a comment |
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$begingroup$
Where else could we put the $T$? $A_T$ looks in the context of matrices like the $T$th component of a vector. I suppose we could use ${}^TA$ or ${}_TA$, or dispense with $T$ altogether with notation such as $bar{A}$. Good luck keeping track of the difference between transposes and Hermitian adjoints of complex matrices then, though.
$endgroup$
– J.G.
Jan 6 at 17:05
$begingroup$
In fact some sources do use ${}^TA$. Other sources use a prime to indicate the transpose, with the obvious potential for confusion.
$endgroup$
– amd
Jan 6 at 21:08
$begingroup$
@J.G. What about T$(A)$
$endgroup$
– Benjamin Thoburn
Jan 6 at 21:37