Outer Product of Two Matrices?
$begingroup$
How would I go about calculating the outer product of two matrices of 2 dimensions each? From what I can find, outer product seems to be the product of two vectors, $u$ and the transpose of another vector, $v^T$.
As an example, how would I calculate the outer product of $A$ and $B$, where
$$A = begin{pmatrix}1 & 2 \ 3 & 4end{pmatrix} qquad B = begin{pmatrix}5 & 6 & 7 \ 8 & 9 & 10end{pmatrix}$$
matrices tensor-products
edited Oct 14 '14 at 16:25
davcha
1,062417
asked Oct 14 '14 at 16:17
user2049004user2049004
3441313
$endgroup$
add a comment |
$begingroup$
How would I go about calculating the outer product of two matrices of 2 dimensions each? From what I can find, outer product seems to be the product of two vectors, $u$ and the transpose of another vector, $v^T$.
As an example, how would I calculate the outer product of $A$ and $B$, where
$$A = begin{pmatrix}1 & 2 \ 3 & 4end{pmatrix} qquad B = begin{pmatrix}5 & 6 & 7 \ 8 & 9 & 10end{pmatrix}$$
matrices tensor-products
edited Oct 14 '14 at 16:25
davcha
1,062417
asked Oct 14 '14 at 16:17
user2049004user2049004
3441313
$endgroup$
add a comment |
$begingroup$
How would I go about calculating the outer product of two matrices of 2 dimensions each? From what I can find, outer product seems to be the product of two vectors, $u$ and the transpose of another vector, $v^T$.
As an example, how would I calculate the outer product of $A$ and $B$, where
$$A = begin{pmatrix}1 & 2 \ 3 & 4end{pmatrix} qquad B = begin{pmatrix}5 & 6 & 7 \ 8 & 9 & 10end{pmatrix}$$
matrices tensor-products
edited Oct 14 '14 at 16:25
davcha
1,062417
asked Oct 14 '14 at 16:17
user2049004user2049004
3441313
$endgroup$
How would I go about calculating the outer product of two matrices of 2 dimensions each? From what I can find, outer product seems to be the product of two vectors, $u$ and the transpose of another vector, $v^T$.
As an example, how would I calculate the outer product of $A$ and $B$, where
$$A = begin{pmatrix}1 & 2 \ 3 & 4end{pmatrix} qquad B = begin{pmatrix}5 & 6 & 7 \ 8 & 9 & 10end{pmatrix}$$
matrices tensor-products
matrices tensor-products
edited Oct 14 '14 at 16:25
davcha
1,062417
asked Oct 14 '14 at 16:17
user2049004user2049004
3441313
edited Oct 14 '14 at 16:25
davcha
1,062417
asked Oct 14 '14 at 16:17
user2049004user2049004
3441313
edited Oct 14 '14 at 16:25
davcha
1,062417
edited Oct 14 '14 at 16:25
davcha
1,062417
edited Oct 14 '14 at 16:25
davcha
1,062417
1,062417
asked Oct 14 '14 at 16:17
user2049004user2049004
3441313
asked Oct 14 '14 at 16:17
user2049004user2049004
3441313
asked Oct 14 '14 at 16:17
user2049004user2049004
3441313
3441313
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
The outer product usually refers to the tensor product of vectors.
If you want something like the outer product between a $m times n$ matrix $A$ and a $ptimes q$ matrix $B$, you can see the generalization of outer product, which is the kronecker product. It is noted $A otimes B$ and equals:
$$A otimes B = begin{pmatrix}a_{11}B & dots & a_{1n}B \ vdots & ddots & vdots \ a_{m1}B & dots & a_{mn}Bend{pmatrix}$$
answered Oct 14 '14 at 16:34
davchadavcha
1,062417
$endgroup$
add a comment |
$begingroup$
To extend davcha's answer, for your specific example, you would get:
$$Aotimes B=
left(
begin{array}{cc}
left(
begin{array}{ccc}
5 & 6 & 7 \
8 & 9 & 10 \
end{array}
right) & left(
begin{array}{ccc}
10 & 12 & 14 \
16 & 18 & 20 \
end{array}
right) \
left(
begin{array}{ccc}
15 & 18 & 21 \
24 & 27 & 30 \
end{array}
right) & left(
begin{array}{ccc}
20 & 24 & 28 \
32 & 36 & 40 \
end{array}
right) \
end{array}
right)
$$
answered Nov 1 '15 at 13:58
Sandu UrsuSandu Ursu
183114
$endgroup$
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
$begingroup$
The outer product usually refers to the tensor product of vectors.
If you want something like the outer product between a $m times n$ matrix $A$ and a $ptimes q$ matrix $B$, you can see the generalization of outer product, which is the kronecker product. It is noted $A otimes B$ and equals:
$$A otimes B = begin{pmatrix}a_{11}B & dots & a_{1n}B \ vdots & ddots & vdots \ a_{m1}B & dots & a_{mn}Bend{pmatrix}$$
answered Oct 14 '14 at 16:34
davchadavcha
1,062417
$endgroup$
add a comment |
$begingroup$
The outer product usually refers to the tensor product of vectors.
If you want something like the outer product between a $m times n$ matrix $A$ and a $ptimes q$ matrix $B$, you can see the generalization of outer product, which is the kronecker product. It is noted $A otimes B$ and equals:
$$A otimes B = begin{pmatrix}a_{11}B & dots & a_{1n}B \ vdots & ddots & vdots \ a_{m1}B & dots & a_{mn}Bend{pmatrix}$$
answered Oct 14 '14 at 16:34
davchadavcha
1,062417
$endgroup$
add a comment |
$begingroup$
The outer product usually refers to the tensor product of vectors.
If you want something like the outer product between a $m times n$ matrix $A$ and a $ptimes q$ matrix $B$, you can see the generalization of outer product, which is the kronecker product. It is noted $A otimes B$ and equals:
$$A otimes B = begin{pmatrix}a_{11}B & dots & a_{1n}B \ vdots & ddots & vdots \ a_{m1}B & dots & a_{mn}Bend{pmatrix}$$
answered Oct 14 '14 at 16:34
davchadavcha
1,062417
$endgroup$
The outer product usually refers to the tensor product of vectors.
If you want something like the outer product between a $m times n$ matrix $A$ and a $ptimes q$ matrix $B$, you can see the generalization of outer product, which is the kronecker product. It is noted $A otimes B$ and equals:
$$A otimes B = begin{pmatrix}a_{11}B & dots & a_{1n}B \ vdots & ddots & vdots \ a_{m1}B & dots & a_{mn}Bend{pmatrix}$$
answered Oct 14 '14 at 16:34
davchadavcha
1,062417
edited Oct 14 '14 at 16:39
answered Oct 14 '14 at 16:34
davchadavcha
1,062417
answered Oct 14 '14 at 16:34
davchadavcha
1,062417
answered Oct 14 '14 at 16:34
davchadavcha
1,062417
1,062417
add a comment |
add a comment |
$begingroup$
To extend davcha's answer, for your specific example, you would get:
$$Aotimes B=
left(
begin{array}{cc}
left(
begin{array}{ccc}
5 & 6 & 7 \
8 & 9 & 10 \
end{array}
right) & left(
begin{array}{ccc}
10 & 12 & 14 \
16 & 18 & 20 \
end{array}
right) \
left(
begin{array}{ccc}
15 & 18 & 21 \
24 & 27 & 30 \
end{array}
right) & left(
begin{array}{ccc}
20 & 24 & 28 \
32 & 36 & 40 \
end{array}
right) \
end{array}
right)
$$
answered Nov 1 '15 at 13:58
Sandu UrsuSandu Ursu
183114
$endgroup$
add a comment |
$begingroup$
To extend davcha's answer, for your specific example, you would get:
$$Aotimes B=
left(
begin{array}{cc}
left(
begin{array}{ccc}
5 & 6 & 7 \
8 & 9 & 10 \
end{array}
right) & left(
begin{array}{ccc}
10 & 12 & 14 \
16 & 18 & 20 \
end{array}
right) \
left(
begin{array}{ccc}
15 & 18 & 21 \
24 & 27 & 30 \
end{array}
right) & left(
begin{array}{ccc}
20 & 24 & 28 \
32 & 36 & 40 \
end{array}
right) \
end{array}
right)
$$
answered Nov 1 '15 at 13:58
Sandu UrsuSandu Ursu
183114
$endgroup$
add a comment |
$begingroup$
To extend davcha's answer, for your specific example, you would get:
$$Aotimes B=
left(
begin{array}{cc}
left(
begin{array}{ccc}
5 & 6 & 7 \
8 & 9 & 10 \
end{array}
right) & left(
begin{array}{ccc}
10 & 12 & 14 \
16 & 18 & 20 \
end{array}
right) \
left(
begin{array}{ccc}
15 & 18 & 21 \
24 & 27 & 30 \
end{array}
right) & left(
begin{array}{ccc}
20 & 24 & 28 \
32 & 36 & 40 \
end{array}
right) \
end{array}
right)
$$
answered Nov 1 '15 at 13:58
Sandu UrsuSandu Ursu
183114
$endgroup$
To extend davcha's answer, for your specific example, you would get:
$$Aotimes B=
left(
begin{array}{cc}
left(
begin{array}{ccc}
5 & 6 & 7 \
8 & 9 & 10 \
end{array}
right) & left(
begin{array}{ccc}
10 & 12 & 14 \
16 & 18 & 20 \
end{array}
right) \
left(
begin{array}{ccc}
15 & 18 & 21 \
24 & 27 & 30 \
end{array}
right) & left(
begin{array}{ccc}
20 & 24 & 28 \
32 & 36 & 40 \
end{array}
right) \
end{array}
right)
$$
answered Nov 1 '15 at 13:58
Sandu UrsuSandu Ursu
183114
answered Nov 1 '15 at 13:58
Sandu UrsuSandu Ursu
183114
answered Nov 1 '15 at 13:58
Sandu UrsuSandu Ursu
183114
answered Nov 1 '15 at 13:58
Sandu UrsuSandu Ursu
183114
183114
add a comment |
add a comment |
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