Rewriting a quadratic Matrix equation as a quadratic vector equationConvexity of a complicated functionExpressing Quadratic Form for a Matrix Inverse using Summation SymbolsFull Rank Matrix with a specific constructionMatrix Multiplication - Product of [Row or Column Vector] and Matrix [Lay P94, Strang P59]How to calculate a vector of quadratic forms (matrix algebra)Conditions to preserve Laplacian matrixBuilding matrix so that the inner product of columns results in an element of another matrixMatrix with only real eigenvalues is similar to upper triangular matrixNumerator layout for derivatives and the chain ruleHelp to find a factorization of a matrix into a product and sum of matricesRepresentation of a matrix (tensor)
Was it really inappropriate to write a pull request for the company I interviewed with?
Create chunks from an array
Writing text next to a table
Can one live in the U.S. and not use a credit card?
What should I do when a paper is published similar to my PhD thesis without citation?
How do I increase the number of TTY consoles?
Do Paladin Auras of Differing Oaths Stack?
Boss Telling direct supervisor I snitched
Volume of hyperbola revolved about the y -axis
How to copy the rest of lines of a file to another file
Has a sovereign Communist government ever run, and conceded loss, on a fair election?
Doublet with ladder line vs coax w.r.t. noise
Computation logic of Partway in TikZ
Can the Witch Sight warlock invocation see through the Mirror Image spell?
What can I do if someone tampers with my SSH public key?
How to educate team mate to take screenshots for bugs with out unwanted stuff
How should I solve this integral with changing parameters?
Are these two graphs isomorphic? Why/Why not?
Either of .... (Plural/Singular)
How do we create new idioms and use them in a novel?
What was so special about The Piano that Ada was willing to do anything to have it?
How can a demon take control of a human body during REM sleep?
Why is there an extra space when I type "ls" on the Desktop?
When to use a QR code on a business card?
Rewriting a quadratic Matrix equation as a quadratic vector equation
Convexity of a complicated functionExpressing Quadratic Form for a Matrix Inverse using Summation SymbolsFull Rank Matrix with a specific constructionMatrix Multiplication - Product of [Row or Column Vector] and Matrix [Lay P94, Strang P59]How to calculate a vector of quadratic forms (matrix algebra)Conditions to preserve Laplacian matrixBuilding matrix so that the inner product of columns results in an element of another matrixMatrix with only real eigenvalues is similar to upper triangular matrixNumerator layout for derivatives and the chain ruleHelp to find a factorization of a matrix into a product and sum of matricesRepresentation of a matrix (tensor)
$begingroup$
Consider the set of $N times N$ matrices $W_i_i=1^i=L$, set of $N times 1$ vectors $g_i_i=1^i=L$ and $h_i_i=1^i=L$. Now consider the following sum
beginalign
S=sum_isum_jg_i^HW_ih_ih_j^HW_j^Hg_j
endalign
where the summation runs through all $L$ for all $i,j$. Clearly, this equation is quadratic in the matrix variables $W_i_i=1^i=L$. Now define the column vector
beginalign
w=beginbmatrix operatornamevec(W_1) \ operatornamevec(W_2) \ vdots \ operatornamevec(W_L) endbmatrix
endalign
where for a matrix $A$, $operatornamevec(A)$ denotes the column vector containing the columns of $A$ starting from the first column. The question is, can we write
beginalign
S=w^HQw
endalign
where $Q$ is a matrix which is a function of $g_i_i=1^i=L$ and $h_i_i=1^i=L$. If so, what is the structure of $Q$?
linear-algebra matrices convex-optimization quadratic-forms block-matrices
edited yesterday
Rócherz
2,8912821
asked Apr 1 '13 at 17:30
dineshdileepdineshdileep
5,98611935
$endgroup$
add a comment |
$begingroup$
Consider the set of $N times N$ matrices $W_i_i=1^i=L$, set of $N times 1$ vectors $g_i_i=1^i=L$ and $h_i_i=1^i=L$. Now consider the following sum
beginalign
S=sum_isum_jg_i^HW_ih_ih_j^HW_j^Hg_j
endalign
where the summation runs through all $L$ for all $i,j$. Clearly, this equation is quadratic in the matrix variables $W_i_i=1^i=L$. Now define the column vector
beginalign
w=beginbmatrix operatornamevec(W_1) \ operatornamevec(W_2) \ vdots \ operatornamevec(W_L) endbmatrix
endalign
where for a matrix $A$, $operatornamevec(A)$ denotes the column vector containing the columns of $A$ starting from the first column. The question is, can we write
beginalign
S=w^HQw
endalign
where $Q$ is a matrix which is a function of $g_i_i=1^i=L$ and $h_i_i=1^i=L$. If so, what is the structure of $Q$?
linear-algebra matrices convex-optimization quadratic-forms block-matrices
edited yesterday
Rócherz
2,8912821
asked Apr 1 '13 at 17:30
dineshdileepdineshdileep
5,98611935
$endgroup$
add a comment |
$begingroup$
Consider the set of $N times N$ matrices $W_i_i=1^i=L$, set of $N times 1$ vectors $g_i_i=1^i=L$ and $h_i_i=1^i=L$. Now consider the following sum
beginalign
S=sum_isum_jg_i^HW_ih_ih_j^HW_j^Hg_j
endalign
where the summation runs through all $L$ for all $i,j$. Clearly, this equation is quadratic in the matrix variables $W_i_i=1^i=L$. Now define the column vector
beginalign
w=beginbmatrix operatornamevec(W_1) \ operatornamevec(W_2) \ vdots \ operatornamevec(W_L) endbmatrix
endalign
where for a matrix $A$, $operatornamevec(A)$ denotes the column vector containing the columns of $A$ starting from the first column. The question is, can we write
beginalign
S=w^HQw
endalign
where $Q$ is a matrix which is a function of $g_i_i=1^i=L$ and $h_i_i=1^i=L$. If so, what is the structure of $Q$?
linear-algebra matrices convex-optimization quadratic-forms block-matrices
edited yesterday
Rócherz
2,8912821
asked Apr 1 '13 at 17:30
dineshdileepdineshdileep
5,98611935
$endgroup$
Consider the set of $N times N$ matrices $W_i_i=1^i=L$, set of $N times 1$ vectors $g_i_i=1^i=L$ and $h_i_i=1^i=L$. Now consider the following sum
beginalign
S=sum_isum_jg_i^HW_ih_ih_j^HW_j^Hg_j
endalign
where the summation runs through all $L$ for all $i,j$. Clearly, this equation is quadratic in the matrix variables $W_i_i=1^i=L$. Now define the column vector
beginalign
w=beginbmatrix operatornamevec(W_1) \ operatornamevec(W_2) \ vdots \ operatornamevec(W_L) endbmatrix
endalign
where for a matrix $A$, $operatornamevec(A)$ denotes the column vector containing the columns of $A$ starting from the first column. The question is, can we write
beginalign
S=w^HQw
endalign
where $Q$ is a matrix which is a function of $g_i_i=1^i=L$ and $h_i_i=1^i=L$. If so, what is the structure of $Q$?
linear-algebra matrices convex-optimization quadratic-forms block-matrices
linear-algebra matrices convex-optimization quadratic-forms block-matrices
edited yesterday
Rócherz
2,8912821
asked Apr 1 '13 at 17:30
dineshdileepdineshdileep
5,98611935
edited yesterday
Rócherz
2,8912821
asked Apr 1 '13 at 17:30
dineshdileepdineshdileep
5,98611935
edited yesterday
Rócherz
2,8912821
edited yesterday
Rócherz
2,8912821
edited yesterday
Rócherz
2,8912821
2,8912821
asked Apr 1 '13 at 17:30
dineshdileepdineshdileep
5,98611935
asked Apr 1 '13 at 17:30
dineshdileepdineshdileep
5,98611935
asked Apr 1 '13 at 17:30
dineshdileepdineshdileep
5,98611935
5,98611935
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
beginalign
S&=sum_isum_jg_i^HW_ih_ih_j^HW_j^Hg_j\
&=sum_isum_joperatornametrace(g_jg_i^HW_ih_ih_j^HW_j^H)\
&=sum_isum_joperatornamevec(W_j)^H operatornamevec(g_jg_i^HW_ih_ih_j^H)\
&qquadqquadqquadbecause operatornametrace(AB^H)=operatornametrace(A^HB)=operatornamevec(A)^Hoperatornamevec(B)\
& \
&=sum_isum_joperatornamevec(W_j)^H left((h_ih_j^H)^Totimes(g_jg_i^H)right)operatornamevec(W_i)\
&qquadqquadqquadbecause operatornamevec(ABC)=(C^Totimes A)operatornamevec(B)\
& \
&=sum_isum_joperatornamevec(W_j)^H left((barh_jh_i^T)otimes(g_jg_i^H)right)operatornamevec(W_i)\
&=w^H Qw,
endalign
where $Q$ is a block matrix whose $(j,i)$-th (note: not $(i,j)$-th) subblock is $(barh_jh_i^T)otimes(g_jg_i^H)$.
edited yesterday
Rócherz
2,8912821
answered Apr 1 '13 at 18:13
user1551user1551
73.5k566129
$endgroup$
$begingroup$
you are always reliable!!!
$endgroup$
– dineshdileep
Apr 2 '13 at 8:50
$begingroup$
@dineshdileep What? Who knows if some mistakes are lurking around in some shadowy places. You should double-check the claimed result.
$endgroup$
– user1551
Apr 2 '13 at 16:12
$begingroup$
I will definitely do that.
$endgroup$
– dineshdileep
Apr 3 '13 at 4:17
$begingroup$
Can you explain (mathematically) the second last step, where you switch to the block matrix. (I almost have it intuitively, but would like to know a rigorous one).
$endgroup$
– dineshdileep
Apr 3 '13 at 4:46
1
$begingroup$
Let $w_j=operatornamevec(W_j)$. Then $w^T=(w_1^T,ldots,w_n^T)$. Partition $Q$ into subblocks, each of size $ntimes n$. Call the $(j,i)$-th block $Q_ji$. Then by $w^HQw=sum_isum_j w_j^H Q_ji w_i$. So, by comparing coefficients, we should set $Q_ji=(barh_jh_i^T)otimes(g_jg_i^H)$.
$endgroup$
– user1551
Apr 3 '13 at 20:51
|
show 1 more comment
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f348302%2frewriting-a-quadratic-matrix-equation-as-a-quadratic-vector-equation%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
beginalign
S&=sum_isum_jg_i^HW_ih_ih_j^HW_j^Hg_j\
&=sum_isum_joperatornametrace(g_jg_i^HW_ih_ih_j^HW_j^H)\
&=sum_isum_joperatornamevec(W_j)^H operatornamevec(g_jg_i^HW_ih_ih_j^H)\
&qquadqquadqquadbecause operatornametrace(AB^H)=operatornametrace(A^HB)=operatornamevec(A)^Hoperatornamevec(B)\
& \
&=sum_isum_joperatornamevec(W_j)^H left((h_ih_j^H)^Totimes(g_jg_i^H)right)operatornamevec(W_i)\
&qquadqquadqquadbecause operatornamevec(ABC)=(C^Totimes A)operatornamevec(B)\
& \
&=sum_isum_joperatornamevec(W_j)^H left((barh_jh_i^T)otimes(g_jg_i^H)right)operatornamevec(W_i)\
&=w^H Qw,
endalign
where $Q$ is a block matrix whose $(j,i)$-th (note: not $(i,j)$-th) subblock is $(barh_jh_i^T)otimes(g_jg_i^H)$.
edited yesterday
Rócherz
2,8912821
answered Apr 1 '13 at 18:13
user1551user1551
73.5k566129
$endgroup$
$begingroup$
you are always reliable!!!
$endgroup$
– dineshdileep
Apr 2 '13 at 8:50
$begingroup$
@dineshdileep What? Who knows if some mistakes are lurking around in some shadowy places. You should double-check the claimed result.
$endgroup$
– user1551
Apr 2 '13 at 16:12
$begingroup$
I will definitely do that.
$endgroup$
– dineshdileep
Apr 3 '13 at 4:17
$begingroup$
Can you explain (mathematically) the second last step, where you switch to the block matrix. (I almost have it intuitively, but would like to know a rigorous one).
$endgroup$
– dineshdileep
Apr 3 '13 at 4:46
1
$begingroup$
Let $w_j=operatornamevec(W_j)$. Then $w^T=(w_1^T,ldots,w_n^T)$. Partition $Q$ into subblocks, each of size $ntimes n$. Call the $(j,i)$-th block $Q_ji$. Then by $w^HQw=sum_isum_j w_j^H Q_ji w_i$. So, by comparing coefficients, we should set $Q_ji=(barh_jh_i^T)otimes(g_jg_i^H)$.
$endgroup$
– user1551
Apr 3 '13 at 20:51
|
show 1 more comment
$begingroup$
beginalign
S&=sum_isum_jg_i^HW_ih_ih_j^HW_j^Hg_j\
&=sum_isum_joperatornametrace(g_jg_i^HW_ih_ih_j^HW_j^H)\
&=sum_isum_joperatornamevec(W_j)^H operatornamevec(g_jg_i^HW_ih_ih_j^H)\
&qquadqquadqquadbecause operatornametrace(AB^H)=operatornametrace(A^HB)=operatornamevec(A)^Hoperatornamevec(B)\
& \
&=sum_isum_joperatornamevec(W_j)^H left((h_ih_j^H)^Totimes(g_jg_i^H)right)operatornamevec(W_i)\
&qquadqquadqquadbecause operatornamevec(ABC)=(C^Totimes A)operatornamevec(B)\
& \
&=sum_isum_joperatornamevec(W_j)^H left((barh_jh_i^T)otimes(g_jg_i^H)right)operatornamevec(W_i)\
&=w^H Qw,
endalign
where $Q$ is a block matrix whose $(j,i)$-th (note: not $(i,j)$-th) subblock is $(barh_jh_i^T)otimes(g_jg_i^H)$.
edited yesterday
Rócherz
2,8912821
answered Apr 1 '13 at 18:13
user1551user1551
73.5k566129
$endgroup$
$begingroup$
you are always reliable!!!
$endgroup$
– dineshdileep
Apr 2 '13 at 8:50
$begingroup$
@dineshdileep What? Who knows if some mistakes are lurking around in some shadowy places. You should double-check the claimed result.
$endgroup$
– user1551
Apr 2 '13 at 16:12
$begingroup$
I will definitely do that.
$endgroup$
– dineshdileep
Apr 3 '13 at 4:17
$begingroup$
Can you explain (mathematically) the second last step, where you switch to the block matrix. (I almost have it intuitively, but would like to know a rigorous one).
$endgroup$
– dineshdileep
Apr 3 '13 at 4:46
1
$begingroup$
Let $w_j=operatornamevec(W_j)$. Then $w^T=(w_1^T,ldots,w_n^T)$. Partition $Q$ into subblocks, each of size $ntimes n$. Call the $(j,i)$-th block $Q_ji$. Then by $w^HQw=sum_isum_j w_j^H Q_ji w_i$. So, by comparing coefficients, we should set $Q_ji=(barh_jh_i^T)otimes(g_jg_i^H)$.
$endgroup$
– user1551
Apr 3 '13 at 20:51
|
show 1 more comment
$begingroup$
beginalign
S&=sum_isum_jg_i^HW_ih_ih_j^HW_j^Hg_j\
&=sum_isum_joperatornametrace(g_jg_i^HW_ih_ih_j^HW_j^H)\
&=sum_isum_joperatornamevec(W_j)^H operatornamevec(g_jg_i^HW_ih_ih_j^H)\
&qquadqquadqquadbecause operatornametrace(AB^H)=operatornametrace(A^HB)=operatornamevec(A)^Hoperatornamevec(B)\
& \
&=sum_isum_joperatornamevec(W_j)^H left((h_ih_j^H)^Totimes(g_jg_i^H)right)operatornamevec(W_i)\
&qquadqquadqquadbecause operatornamevec(ABC)=(C^Totimes A)operatornamevec(B)\
& \
&=sum_isum_joperatornamevec(W_j)^H left((barh_jh_i^T)otimes(g_jg_i^H)right)operatornamevec(W_i)\
&=w^H Qw,
endalign
where $Q$ is a block matrix whose $(j,i)$-th (note: not $(i,j)$-th) subblock is $(barh_jh_i^T)otimes(g_jg_i^H)$.
edited yesterday
Rócherz
2,8912821
answered Apr 1 '13 at 18:13
user1551user1551
73.5k566129
$endgroup$
beginalign
S&=sum_isum_jg_i^HW_ih_ih_j^HW_j^Hg_j\
&=sum_isum_joperatornametrace(g_jg_i^HW_ih_ih_j^HW_j^H)\
&=sum_isum_joperatornamevec(W_j)^H operatornamevec(g_jg_i^HW_ih_ih_j^H)\
&qquadqquadqquadbecause operatornametrace(AB^H)=operatornametrace(A^HB)=operatornamevec(A)^Hoperatornamevec(B)\
& \
&=sum_isum_joperatornamevec(W_j)^H left((h_ih_j^H)^Totimes(g_jg_i^H)right)operatornamevec(W_i)\
&qquadqquadqquadbecause operatornamevec(ABC)=(C^Totimes A)operatornamevec(B)\
& \
&=sum_isum_joperatornamevec(W_j)^H left((barh_jh_i^T)otimes(g_jg_i^H)right)operatornamevec(W_i)\
&=w^H Qw,
endalign
where $Q$ is a block matrix whose $(j,i)$-th (note: not $(i,j)$-th) subblock is $(barh_jh_i^T)otimes(g_jg_i^H)$.
edited yesterday
Rócherz
2,8912821
answered Apr 1 '13 at 18:13
user1551user1551
73.5k566129
edited yesterday
Rócherz
2,8912821
edited yesterday
Rócherz
2,8912821
edited yesterday
Rócherz
2,8912821
2,8912821
answered Apr 1 '13 at 18:13
user1551user1551
73.5k566129
answered Apr 1 '13 at 18:13
user1551user1551
73.5k566129
answered Apr 1 '13 at 18:13
user1551user1551
73.5k566129
73.5k566129
$begingroup$
you are always reliable!!!
$endgroup$
– dineshdileep
Apr 2 '13 at 8:50
$begingroup$
@dineshdileep What? Who knows if some mistakes are lurking around in some shadowy places. You should double-check the claimed result.
$endgroup$
– user1551
Apr 2 '13 at 16:12
$begingroup$
I will definitely do that.
$endgroup$
– dineshdileep
Apr 3 '13 at 4:17
$begingroup$
Can you explain (mathematically) the second last step, where you switch to the block matrix. (I almost have it intuitively, but would like to know a rigorous one).
$endgroup$
– dineshdileep
Apr 3 '13 at 4:46
1
$begingroup$
Let $w_j=operatornamevec(W_j)$. Then $w^T=(w_1^T,ldots,w_n^T)$. Partition $Q$ into subblocks, each of size $ntimes n$. Call the $(j,i)$-th block $Q_ji$. Then by $w^HQw=sum_isum_j w_j^H Q_ji w_i$. So, by comparing coefficients, we should set $Q_ji=(barh_jh_i^T)otimes(g_jg_i^H)$.
$endgroup$
– user1551
Apr 3 '13 at 20:51
|
show 1 more comment
$begingroup$
you are always reliable!!!
$endgroup$
– dineshdileep
Apr 2 '13 at 8:50
$begingroup$
@dineshdileep What? Who knows if some mistakes are lurking around in some shadowy places. You should double-check the claimed result.
$endgroup$
– user1551
Apr 2 '13 at 16:12
$begingroup$
I will definitely do that.
$endgroup$
– dineshdileep
Apr 3 '13 at 4:17
$begingroup$
Can you explain (mathematically) the second last step, where you switch to the block matrix. (I almost have it intuitively, but would like to know a rigorous one).
$endgroup$
– dineshdileep
Apr 3 '13 at 4:46
1
$begingroup$
Let $w_j=operatornamevec(W_j)$. Then $w^T=(w_1^T,ldots,w_n^T)$. Partition $Q$ into subblocks, each of size $ntimes n$. Call the $(j,i)$-th block $Q_ji$. Then by $w^HQw=sum_isum_j w_j^H Q_ji w_i$. So, by comparing coefficients, we should set $Q_ji=(barh_jh_i^T)otimes(g_jg_i^H)$.
$endgroup$
– user1551
Apr 3 '13 at 20:51
$begingroup$
you are always reliable!!!
$endgroup$
– dineshdileep
Apr 2 '13 at 8:50
$begingroup$
you are always reliable!!!
$endgroup$
– dineshdileep
Apr 2 '13 at 8:50
$begingroup$
@dineshdileep What? Who knows if some mistakes are lurking around in some shadowy places. You should double-check the claimed result.
$endgroup$
– user1551
Apr 2 '13 at 16:12
$begingroup$
@dineshdileep What? Who knows if some mistakes are lurking around in some shadowy places. You should double-check the claimed result.
$endgroup$
– user1551
Apr 2 '13 at 16:12
$begingroup$
I will definitely do that.
$endgroup$
– dineshdileep
Apr 3 '13 at 4:17
$begingroup$
I will definitely do that.
$endgroup$
– dineshdileep
Apr 3 '13 at 4:17
$begingroup$
Can you explain (mathematically) the second last step, where you switch to the block matrix. (I almost have it intuitively, but would like to know a rigorous one).
$endgroup$
– dineshdileep
Apr 3 '13 at 4:46
$begingroup$
Can you explain (mathematically) the second last step, where you switch to the block matrix. (I almost have it intuitively, but would like to know a rigorous one).
$endgroup$
– dineshdileep
Apr 3 '13 at 4:46
1
1
$begingroup$
Let $w_j=operatornamevec(W_j)$. Then $w^T=(w_1^T,ldots,w_n^T)$. Partition $Q$ into subblocks, each of size $ntimes n$. Call the $(j,i)$-th block $Q_ji$. Then by $w^HQw=sum_isum_j w_j^H Q_ji w_i$. So, by comparing coefficients, we should set $Q_ji=(barh_jh_i^T)otimes(g_jg_i^H)$.
$endgroup$
– user1551
Apr 3 '13 at 20:51
$begingroup$
Let $w_j=operatornamevec(W_j)$. Then $w^T=(w_1^T,ldots,w_n^T)$. Partition $Q$ into subblocks, each of size $ntimes n$. Call the $(j,i)$-th block $Q_ji$. Then by $w^HQw=sum_isum_j w_j^H Q_ji w_i$. So, by comparing coefficients, we should set $Q_ji=(barh_jh_i^T)otimes(g_jg_i^H)$.
$endgroup$
– user1551
Apr 3 '13 at 20:51
|
show 1 more comment
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f348302%2frewriting-a-quadratic-matrix-equation-as-a-quadratic-vector-equation%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
