Why Jacobian matrix is a special case of alternant matrix?
$begingroup$
I don't quite understand why a standard Jacobian matrix
$$JF(x) = left[{partial F_iover partial x_j}right]_{ij}$$
is alternant matrix.
Because I think Jacobian matrix uses the same $alpha$, or the same variate in the expression, so it is not a alternant matrix.
linear-algebra matrices
edited Jan 5 at 7:03
Mostafa Ayaz
15.5k3939
asked Jan 5 at 5:27
ArtificiallyIntelligenceArtificiallyIntelligence
291111
$endgroup$
add a comment |
$begingroup$
I don't quite understand why a standard Jacobian matrix
$$JF(x) = left[{partial F_iover partial x_j}right]_{ij}$$
is alternant matrix.
Because I think Jacobian matrix uses the same $alpha$, or the same variate in the expression, so it is not a alternant matrix.
linear-algebra matrices
edited Jan 5 at 7:03
Mostafa Ayaz
15.5k3939
asked Jan 5 at 5:27
ArtificiallyIntelligenceArtificiallyIntelligence
291111
$endgroup$
add a comment |
$begingroup$
I don't quite understand why a standard Jacobian matrix
$$JF(x) = left[{partial F_iover partial x_j}right]_{ij}$$
is alternant matrix.
Because I think Jacobian matrix uses the same $alpha$, or the same variate in the expression, so it is not a alternant matrix.
linear-algebra matrices
edited Jan 5 at 7:03
Mostafa Ayaz
15.5k3939
asked Jan 5 at 5:27
ArtificiallyIntelligenceArtificiallyIntelligence
291111
$endgroup$
I don't quite understand why a standard Jacobian matrix
$$JF(x) = left[{partial F_iover partial x_j}right]_{ij}$$
is alternant matrix.
Because I think Jacobian matrix uses the same $alpha$, or the same variate in the expression, so it is not a alternant matrix.
linear-algebra matrices
linear-algebra matrices
edited Jan 5 at 7:03
Mostafa Ayaz
15.5k3939
asked Jan 5 at 5:27
ArtificiallyIntelligenceArtificiallyIntelligence
291111
edited Jan 5 at 7:03
Mostafa Ayaz
15.5k3939
asked Jan 5 at 5:27
ArtificiallyIntelligenceArtificiallyIntelligence
291111
edited Jan 5 at 7:03
Mostafa Ayaz
15.5k3939
edited Jan 5 at 7:03
Mostafa Ayaz
15.5k3939
edited Jan 5 at 7:03
Mostafa Ayaz
15.5k3939
15.5k3939
asked Jan 5 at 5:27
ArtificiallyIntelligenceArtificiallyIntelligence
291111
asked Jan 5 at 5:27
ArtificiallyIntelligenceArtificiallyIntelligence
291111
asked Jan 5 at 5:27
ArtificiallyIntelligenceArtificiallyIntelligence
291111
291111
add a comment |
add a comment |
1 Answer
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$begingroup$
Hint
Define $$f_i(x)={partial F_i(x)over partial x}$$and try to represent $J F(x)$ as a matrix with entries being of form $f_i(x_j)$.
answered Jan 5 at 7:02
Mostafa AyazMostafa Ayaz
15.5k3939
$endgroup$
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Hint
Define $$f_i(x)={partial F_i(x)over partial x}$$and try to represent $J F(x)$ as a matrix with entries being of form $f_i(x_j)$.
answered Jan 5 at 7:02
Mostafa AyazMostafa Ayaz
15.5k3939
$endgroup$
add a comment |
$begingroup$
Hint
Define $$f_i(x)={partial F_i(x)over partial x}$$and try to represent $J F(x)$ as a matrix with entries being of form $f_i(x_j)$.
answered Jan 5 at 7:02
Mostafa AyazMostafa Ayaz
15.5k3939
$endgroup$
add a comment |
$begingroup$
Hint
Define $$f_i(x)={partial F_i(x)over partial x}$$and try to represent $J F(x)$ as a matrix with entries being of form $f_i(x_j)$.
answered Jan 5 at 7:02
Mostafa AyazMostafa Ayaz
15.5k3939
$endgroup$
Hint
Define $$f_i(x)={partial F_i(x)over partial x}$$and try to represent $J F(x)$ as a matrix with entries being of form $f_i(x_j)$.
answered Jan 5 at 7:02
Mostafa AyazMostafa Ayaz
15.5k3939
answered Jan 5 at 7:02
Mostafa AyazMostafa Ayaz
15.5k3939
answered Jan 5 at 7:02
Mostafa AyazMostafa Ayaz
15.5k3939
answered Jan 5 at 7:02
Mostafa AyazMostafa Ayaz
15.5k3939
15.5k3939
add a comment |
add a comment |
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