Mixing
Property on Kronecker product
$begingroup$
I read a paper and there was an equation which was finally derived an equivalent expression as
$$
L = L_{T} otimes I_{G} + I_{T} otimes L_{G} = {color{blue}{L_{T} times L_{G}}} ,
$$
and considering $L_{T} = U_{T}Lambda_{T} U_{T}^{*}$ and $L_{G} = U_{G}Lambda_{G} U_{G}^{*}$, it is obtained
$$
L = {color{red}{(U_{T}otimes U_{G})(Lambda_{T} times Lambda_{G})(U_{T} otimes U_{G})^*}} ,
$$
where $otimes$ accounts for the Kronecker product, $*$ is the Hermitian and $times$ is the Cartesian product.
I am confused how to obtain the results in blue and red. Would you please help me to clarify them?
linear-algebra kronecker-product
asked Jan 3 at 4:08
AminAmin
1,3281719
$endgroup$
add a comment |
$begingroup$
I read a paper and there was an equation which was finally derived an equivalent expression as
$$
L = L_{T} otimes I_{G} + I_{T} otimes L_{G} = {color{blue}{L_{T} times L_{G}}} ,
$$
and considering $L_{T} = U_{T}Lambda_{T} U_{T}^{*}$ and $L_{G} = U_{G}Lambda_{G} U_{G}^{*}$, it is obtained
$$
L = {color{red}{(U_{T}otimes U_{G})(Lambda_{T} times Lambda_{G})(U_{T} otimes U_{G})^*}} ,
$$
where $otimes$ accounts for the Kronecker product, $*$ is the Hermitian and $times$ is the Cartesian product.
I am confused how to obtain the results in blue and red. Would you please help me to clarify them?
linear-algebra kronecker-product
asked Jan 3 at 4:08
AminAmin
1,3281719
$endgroup$
add a comment |
$begingroup$
I read a paper and there was an equation which was finally derived an equivalent expression as
$$
L = L_{T} otimes I_{G} + I_{T} otimes L_{G} = {color{blue}{L_{T} times L_{G}}} ,
$$
and considering $L_{T} = U_{T}Lambda_{T} U_{T}^{*}$ and $L_{G} = U_{G}Lambda_{G} U_{G}^{*}$, it is obtained
$$
L = {color{red}{(U_{T}otimes U_{G})(Lambda_{T} times Lambda_{G})(U_{T} otimes U_{G})^*}} ,
$$
where $otimes$ accounts for the Kronecker product, $*$ is the Hermitian and $times$ is the Cartesian product.
I am confused how to obtain the results in blue and red. Would you please help me to clarify them?
linear-algebra kronecker-product
asked Jan 3 at 4:08
AminAmin
1,3281719
$endgroup$
I read a paper and there was an equation which was finally derived an equivalent expression as
$$
L = L_{T} otimes I_{G} + I_{T} otimes L_{G} = {color{blue}{L_{T} times L_{G}}} ,
$$
and considering $L_{T} = U_{T}Lambda_{T} U_{T}^{*}$ and $L_{G} = U_{G}Lambda_{G} U_{G}^{*}$, it is obtained
$$
L = {color{red}{(U_{T}otimes U_{G})(Lambda_{T} times Lambda_{G})(U_{T} otimes U_{G})^*}} ,
$$
where $otimes$ accounts for the Kronecker product, $*$ is the Hermitian and $times$ is the Cartesian product.
I am confused how to obtain the results in blue and red. Would you please help me to clarify them?
linear-algebra kronecker-product
linear-algebra kronecker-product
asked Jan 3 at 4:08
AminAmin
1,3281719
asked Jan 3 at 4:08
AminAmin
1,3281719
edited Jan 3 at 6:29
Amin
asked Jan 3 at 4:08
AminAmin
1,3281719
asked Jan 3 at 4:08
AminAmin
1,3281719
asked Jan 3 at 4:08
AminAmin
1,3281719
1,3281719
add a comment |
add a comment |
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