Mixing
Product of matrices multiplying each row by corresponding column
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I was wondering if there exists a certain type of matrix multiplication that just multiplies row $i$ by column $i$. For example let be
$$
A=beginbmatrix
a_11 & a_12 & a_13 \
a_21 & a_22 & a_23 \
a_31 & a_32 & a_33 \
endbmatrix
$$
I want to represent the following matrix:
$$
B=beginbmatrix
sum_i=1^3 a_i1^2 & sum_i=1^3 a_i2^2 & sum_i=1^3 a_i3^2 \
endbmatrix
$$
I can define $B=operatornamediag(A^TA)$, but I was wondering if there exists a type of product for representing $B$.
matrices products
edited Jul 28 at 18:04
Daniel Buck
2,2841623
asked Jul 28 at 17:29
coolsv
687
add a comment |Â
up vote
0
down vote
favorite
I was wondering if there exists a certain type of matrix multiplication that just multiplies row $i$ by column $i$. For example let be
$$
A=beginbmatrix
a_11 & a_12 & a_13 \
a_21 & a_22 & a_23 \
a_31 & a_32 & a_33 \
endbmatrix
$$
I want to represent the following matrix:
$$
B=beginbmatrix
sum_i=1^3 a_i1^2 & sum_i=1^3 a_i2^2 & sum_i=1^3 a_i3^2 \
endbmatrix
$$
I can define $B=operatornamediag(A^TA)$, but I was wondering if there exists a type of product for representing $B$.
matrices products
edited Jul 28 at 18:04
Daniel Buck
2,2841623
asked Jul 28 at 17:29
coolsv
687
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I was wondering if there exists a certain type of matrix multiplication that just multiplies row $i$ by column $i$. For example let be
$$
A=beginbmatrix
a_11 & a_12 & a_13 \
a_21 & a_22 & a_23 \
a_31 & a_32 & a_33 \
endbmatrix
$$
I want to represent the following matrix:
$$
B=beginbmatrix
sum_i=1^3 a_i1^2 & sum_i=1^3 a_i2^2 & sum_i=1^3 a_i3^2 \
endbmatrix
$$
I can define $B=operatornamediag(A^TA)$, but I was wondering if there exists a type of product for representing $B$.
matrices products
edited Jul 28 at 18:04
Daniel Buck
2,2841623
asked Jul 28 at 17:29
coolsv
687
I was wondering if there exists a certain type of matrix multiplication that just multiplies row $i$ by column $i$. For example let be
$$
A=beginbmatrix
a_11 & a_12 & a_13 \
a_21 & a_22 & a_23 \
a_31 & a_32 & a_33 \
endbmatrix
$$
I want to represent the following matrix:
$$
B=beginbmatrix
sum_i=1^3 a_i1^2 & sum_i=1^3 a_i2^2 & sum_i=1^3 a_i3^2 \
endbmatrix
$$
I can define $B=operatornamediag(A^TA)$, but I was wondering if there exists a type of product for representing $B$.
matrices products
edited Jul 28 at 18:04
Daniel Buck
2,2841623
asked Jul 28 at 17:29
coolsv
687
edited Jul 28 at 18:04
Daniel Buck
2,2841623
edited Jul 28 at 18:04
Daniel Buck
2,2841623
edited Jul 28 at 18:04
Daniel Buck
2,2841623
2,2841623
asked Jul 28 at 17:29
coolsv
687
asked Jul 28 at 17:29
coolsv
687
asked Jul 28 at 17:29
coolsv
687
687
add a comment |Â
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
1
down vote
accepted
At the top of my head it doesn't seem like such operation would exist! By just for fun you could try to see the properties that such operation should have, maybe you get something interesting out of it!
The only "less known", I put it in quotation marks just because it's not totally true that isn't known but respect to classic matrix multiplication it is, is the Kroneker product defined as: given two matrices $A$ and $B$, their Kronecker product is as follows $$Aotimes B=left(beginmatrixa_11B&a_12B&cdots&a_1nB\a_21B&a_22B&cdots&a_2nB\vdots&vdots&ddots&vdots\a_n1B&a_n2B&cdots&a_nnBendmatrixright)$$
answered Jul 28 at 19:26
Davide Morgante
1,728220
Yeah Davide. I only know the Kronecker product and the Hadamard product! So perhaps there's no such product as you mentioned! Thanks
– coolsv
Jul 29 at 4:44
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
At the top of my head it doesn't seem like such operation would exist! By just for fun you could try to see the properties that such operation should have, maybe you get something interesting out of it!
The only "less known", I put it in quotation marks just because it's not totally true that isn't known but respect to classic matrix multiplication it is, is the Kroneker product defined as: given two matrices $A$ and $B$, their Kronecker product is as follows $$Aotimes B=left(beginmatrixa_11B&a_12B&cdots&a_1nB\a_21B&a_22B&cdots&a_2nB\vdots&vdots&ddots&vdots\a_n1B&a_n2B&cdots&a_nnBendmatrixright)$$
answered Jul 28 at 19:26
Davide Morgante
1,728220
Yeah Davide. I only know the Kronecker product and the Hadamard product! So perhaps there's no such product as you mentioned! Thanks
– coolsv
Jul 29 at 4:44
add a comment |Â
up vote
1
down vote
accepted
At the top of my head it doesn't seem like such operation would exist! By just for fun you could try to see the properties that such operation should have, maybe you get something interesting out of it!
The only "less known", I put it in quotation marks just because it's not totally true that isn't known but respect to classic matrix multiplication it is, is the Kroneker product defined as: given two matrices $A$ and $B$, their Kronecker product is as follows $$Aotimes B=left(beginmatrixa_11B&a_12B&cdots&a_1nB\a_21B&a_22B&cdots&a_2nB\vdots&vdots&ddots&vdots\a_n1B&a_n2B&cdots&a_nnBendmatrixright)$$
answered Jul 28 at 19:26
Davide Morgante
1,728220
Yeah Davide. I only know the Kronecker product and the Hadamard product! So perhaps there's no such product as you mentioned! Thanks
– coolsv
Jul 29 at 4:44
add a comment |Â
up vote
1
down vote
accepted
up vote
1
down vote
accepted
At the top of my head it doesn't seem like such operation would exist! By just for fun you could try to see the properties that such operation should have, maybe you get something interesting out of it!
The only "less known", I put it in quotation marks just because it's not totally true that isn't known but respect to classic matrix multiplication it is, is the Kroneker product defined as: given two matrices $A$ and $B$, their Kronecker product is as follows $$Aotimes B=left(beginmatrixa_11B&a_12B&cdots&a_1nB\a_21B&a_22B&cdots&a_2nB\vdots&vdots&ddots&vdots\a_n1B&a_n2B&cdots&a_nnBendmatrixright)$$
answered Jul 28 at 19:26
Davide Morgante
1,728220
At the top of my head it doesn't seem like such operation would exist! By just for fun you could try to see the properties that such operation should have, maybe you get something interesting out of it!
The only "less known", I put it in quotation marks just because it's not totally true that isn't known but respect to classic matrix multiplication it is, is the Kroneker product defined as: given two matrices $A$ and $B$, their Kronecker product is as follows $$Aotimes B=left(beginmatrixa_11B&a_12B&cdots&a_1nB\a_21B&a_22B&cdots&a_2nB\vdots&vdots&ddots&vdots\a_n1B&a_n2B&cdots&a_nnBendmatrixright)$$
answered Jul 28 at 19:26
Davide Morgante
1,728220
answered Jul 28 at 19:26
Davide Morgante
1,728220
answered Jul 28 at 19:26
Davide Morgante
1,728220
answered Jul 28 at 19:26
Davide Morgante
1,728220
1,728220
Yeah Davide. I only know the Kronecker product and the Hadamard product! So perhaps there's no such product as you mentioned! Thanks
– coolsv
Jul 29 at 4:44
add a comment |Â
Yeah Davide. I only know the Kronecker product and the Hadamard product! So perhaps there's no such product as you mentioned! Thanks
– coolsv
Jul 29 at 4:44
Yeah Davide. I only know the Kronecker product and the Hadamard product! So perhaps there's no such product as you mentioned! Thanks
– coolsv
Jul 29 at 4:44
Yeah Davide. I only know the Kronecker product and the Hadamard product! So perhaps there's no such product as you mentioned! Thanks
– coolsv
Jul 29 at 4:44
add a comment |Â
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