Is there a name given to matrices of the form A'XA or AXA'? A is either symmetric or NOT.
Clash Royale CLAN TAG#URR8PPP
up vote
0
down vote
favorite
I understand that $x'Ax$ is generally called the quadratic form, with $x$ being a vector and $A$ is symmetric.
Is there a name given to matrices of the form $AXA$?
$A$ is symmetric, and $X$ here is a matrix which may not be symmetric.
Edit:
Case 2:
If $A$ is not symmetric and not an identity, is there a name given to any of the forms $A'XA$ or $AXA'$?
symmetric-groups symmetry symmetric-matrices
asked Aug 26 at 7:33
Kay
63
add a comment |Â
up vote
0
down vote
favorite
I understand that $x'Ax$ is generally called the quadratic form, with $x$ being a vector and $A$ is symmetric.
Is there a name given to matrices of the form $AXA$?
$A$ is symmetric, and $X$ here is a matrix which may not be symmetric.
Edit:
Case 2:
If $A$ is not symmetric and not an identity, is there a name given to any of the forms $A'XA$ or $AXA'$?
symmetric-groups symmetry symmetric-matrices
asked Aug 26 at 7:33
Kay
63
All (square) matrices have this form: For any $X$, $X = I X I$.
– Travis
Aug 26 at 7:34
Every matrix can be written in that form by picking the identity for $A$
– Alessandro Codenotti
Aug 26 at 7:34
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I understand that $x'Ax$ is generally called the quadratic form, with $x$ being a vector and $A$ is symmetric.
Is there a name given to matrices of the form $AXA$?
$A$ is symmetric, and $X$ here is a matrix which may not be symmetric.
Edit:
Case 2:
If $A$ is not symmetric and not an identity, is there a name given to any of the forms $A'XA$ or $AXA'$?
symmetric-groups symmetry symmetric-matrices
asked Aug 26 at 7:33
Kay
63
I understand that $x'Ax$ is generally called the quadratic form, with $x$ being a vector and $A$ is symmetric.
Is there a name given to matrices of the form $AXA$?
$A$ is symmetric, and $X$ here is a matrix which may not be symmetric.
Edit:
Case 2:
If $A$ is not symmetric and not an identity, is there a name given to any of the forms $A'XA$ or $AXA'$?
symmetric-groups symmetry symmetric-matrices
asked Aug 26 at 7:33
Kay
63
edited Aug 26 at 7:42
asked Aug 26 at 7:33
Kay
63
asked Aug 26 at 7:33
Kay
63
asked Aug 26 at 7:33
Kay
63
63
All (square) matrices have this form: For any $X$, $X = I X I$.
– Travis
Aug 26 at 7:34
Every matrix can be written in that form by picking the identity for $A$
– Alessandro Codenotti
Aug 26 at 7:34
add a comment |Â
All (square) matrices have this form: For any $X$, $X = I X I$.
– Travis
Aug 26 at 7:34
Every matrix can be written in that form by picking the identity for $A$
– Alessandro Codenotti
Aug 26 at 7:34
All (square) matrices have this form: For any $X$, $X = I X I$.
– Travis
Aug 26 at 7:34
All (square) matrices have this form: For any $X$, $X = I X I$.
– Travis
Aug 26 at 7:34
Every matrix can be written in that form by picking the identity for $A$
– Alessandro Codenotti
Aug 26 at 7:34
Every matrix can be written in that form by picking the identity for $A$
– Alessandro Codenotti
Aug 26 at 7:34
add a comment |Â
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
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
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2894795%2fis-there-a-name-given-to-matrices-of-the-form-axa-or-axa-a-is-either-symmetri%23new-answer', 'question_page');
);
Post as a guest
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
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
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
All (square) matrices have this form: For any $X$, $X = I X I$.
– Travis
Aug 26 at 7:34
Every matrix can be written in that form by picking the identity for $A$
– Alessandro Codenotti
Aug 26 at 7:34