$AA^#=A^#A$ , Complex Matrices
Clash Royale CLAN TAG#URR8PPP
up vote
1
down vote
favorite
If $A$ is an $ntimes n$ invertible matrix of complex functions entries, with the property $AA^#=A^#A$ where $A^#(z)=left(overlineA(barz) right)^T$. Is it true that
$$A B A^#=A^#BA$$
for any $ntimes n$ complex matrix of functions $B$?
If not, when this result could be true?
Thanks in advance.
linear-algebra matrices complex-analysis
add a comment |Â
up vote
1
down vote
favorite
If $A$ is an $ntimes n$ invertible matrix of complex functions entries, with the property $AA^#=A^#A$ where $A^#(z)=left(overlineA(barz) right)^T$. Is it true that
$$A B A^#=A^#BA$$
for any $ntimes n$ complex matrix of functions $B$?
If not, when this result could be true?
Thanks in advance.
linear-algebra matrices complex-analysis
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
If $A$ is an $ntimes n$ invertible matrix of complex functions entries, with the property $AA^#=A^#A$ where $A^#(z)=left(overlineA(barz) right)^T$. Is it true that
$$A B A^#=A^#BA$$
for any $ntimes n$ complex matrix of functions $B$?
If not, when this result could be true?
Thanks in advance.
linear-algebra matrices complex-analysis
If $A$ is an $ntimes n$ invertible matrix of complex functions entries, with the property $AA^#=A^#A$ where $A^#(z)=left(overlineA(barz) right)^T$. Is it true that
$$A B A^#=A^#BA$$
for any $ntimes n$ complex matrix of functions $B$?
If not, when this result could be true?
Thanks in advance.
linear-algebra matrices complex-analysis
asked Aug 16 at 4:37
John
192
192
add a comment |Â
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
1
down vote
E.g. try
$$ A = pmatrixz+i & zcr z & z+icr, A^# = pmatrixz-i & zcr z & z-icr, B = pmatrix1 & 0cr 0 & 0cr $$
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
E.g. try
$$ A = pmatrixz+i & zcr z & z+icr, A^# = pmatrixz-i & zcr z & z-icr, B = pmatrix1 & 0cr 0 & 0cr $$
add a comment |Â
up vote
1
down vote
E.g. try
$$ A = pmatrixz+i & zcr z & z+icr, A^# = pmatrixz-i & zcr z & z-icr, B = pmatrix1 & 0cr 0 & 0cr $$
add a comment |Â
up vote
1
down vote
up vote
1
down vote
E.g. try
$$ A = pmatrixz+i & zcr z & z+icr, A^# = pmatrixz-i & zcr z & z-icr, B = pmatrix1 & 0cr 0 & 0cr $$
E.g. try
$$ A = pmatrixz+i & zcr z & z+icr, A^# = pmatrixz-i & zcr z & z-icr, B = pmatrix1 & 0cr 0 & 0cr $$
answered Aug 16 at 6:20
Robert Israel
305k22201443
305k22201443
add a comment |Â
add a comment |Â
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%2f2884402%2faa-a-a-complex-matrices%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