If $A$ is a positive definite matrix and $textdetB=0$, then $textdet(A+B)$ is positive?
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If $A$ is a positive definite matrix and a symmetric matrix $B$ satisfies $textdetB=0$,
then $textdet(A+B)$ is positive?
I tired to find a counterexample for this, but I couldn't.
determinant positive-definite
add a comment |Â
up vote
0
down vote
favorite
If $A$ is a positive definite matrix and a symmetric matrix $B$ satisfies $textdetB=0$,
then $textdet(A+B)$ is positive?
I tired to find a counterexample for this, but I couldn't.
determinant positive-definite
1
Not sure.. What about A = diag(1,1), B= diag(-1,0)?
â James
Sep 6 at 11:19
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
If $A$ is a positive definite matrix and a symmetric matrix $B$ satisfies $textdetB=0$,
then $textdet(A+B)$ is positive?
I tired to find a counterexample for this, but I couldn't.
determinant positive-definite
If $A$ is a positive definite matrix and a symmetric matrix $B$ satisfies $textdetB=0$,
then $textdet(A+B)$ is positive?
I tired to find a counterexample for this, but I couldn't.
determinant positive-definite
determinant positive-definite
edited Sep 6 at 11:11
asked Sep 6 at 11:03
kayak
576318
576318
1
Not sure.. What about A = diag(1,1), B= diag(-1,0)?
â James
Sep 6 at 11:19
add a comment |Â
1
Not sure.. What about A = diag(1,1), B= diag(-1,0)?
â James
Sep 6 at 11:19
1
1
Not sure.. What about A = diag(1,1), B= diag(-1,0)?
â James
Sep 6 at 11:19
Not sure.. What about A = diag(1,1), B= diag(-1,0)?
â James
Sep 6 at 11:19
add a comment |Â
1 Answer
1
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up vote
0
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accepted
Counterexample:
$$mathbf A=beginpmatrix-2&1\1&-7endpmatrix\mathbf B=beginpmatrix1&3\3&9endpmatrix$$ $det(mathbfA)>0$ and $det(mathbfB)=0$, but $det(mathbfA+mathbfB)=(-1)cdot 2-4cdot 4=-18<0$.
Thanks. Umm actually $B$ was also a symmetric matrix. Is that okay to change the question?
â kayak
Sep 6 at 11:11
@kayak Sure! I'll delete my answer then, and think some more.
â cansomeonehelpmeout
Sep 6 at 11:12
1
As a guide for the future: Editing the question after someone's provided an answer is generally frowned upon, for it makes the original answer look silly, when the real silliness was in being sloppy about asking the question.
â John Hughes
Sep 6 at 12:03
@JohnHughes Oh sorry. Ill keep that in mind.
â kayak
Sep 7 at 4:25
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
accepted
Counterexample:
$$mathbf A=beginpmatrix-2&1\1&-7endpmatrix\mathbf B=beginpmatrix1&3\3&9endpmatrix$$ $det(mathbfA)>0$ and $det(mathbfB)=0$, but $det(mathbfA+mathbfB)=(-1)cdot 2-4cdot 4=-18<0$.
Thanks. Umm actually $B$ was also a symmetric matrix. Is that okay to change the question?
â kayak
Sep 6 at 11:11
@kayak Sure! I'll delete my answer then, and think some more.
â cansomeonehelpmeout
Sep 6 at 11:12
1
As a guide for the future: Editing the question after someone's provided an answer is generally frowned upon, for it makes the original answer look silly, when the real silliness was in being sloppy about asking the question.
â John Hughes
Sep 6 at 12:03
@JohnHughes Oh sorry. Ill keep that in mind.
â kayak
Sep 7 at 4:25
add a comment |Â
up vote
0
down vote
accepted
Counterexample:
$$mathbf A=beginpmatrix-2&1\1&-7endpmatrix\mathbf B=beginpmatrix1&3\3&9endpmatrix$$ $det(mathbfA)>0$ and $det(mathbfB)=0$, but $det(mathbfA+mathbfB)=(-1)cdot 2-4cdot 4=-18<0$.
Thanks. Umm actually $B$ was also a symmetric matrix. Is that okay to change the question?
â kayak
Sep 6 at 11:11
@kayak Sure! I'll delete my answer then, and think some more.
â cansomeonehelpmeout
Sep 6 at 11:12
1
As a guide for the future: Editing the question after someone's provided an answer is generally frowned upon, for it makes the original answer look silly, when the real silliness was in being sloppy about asking the question.
â John Hughes
Sep 6 at 12:03
@JohnHughes Oh sorry. Ill keep that in mind.
â kayak
Sep 7 at 4:25
add a comment |Â
up vote
0
down vote
accepted
up vote
0
down vote
accepted
Counterexample:
$$mathbf A=beginpmatrix-2&1\1&-7endpmatrix\mathbf B=beginpmatrix1&3\3&9endpmatrix$$ $det(mathbfA)>0$ and $det(mathbfB)=0$, but $det(mathbfA+mathbfB)=(-1)cdot 2-4cdot 4=-18<0$.
Counterexample:
$$mathbf A=beginpmatrix-2&1\1&-7endpmatrix\mathbf B=beginpmatrix1&3\3&9endpmatrix$$ $det(mathbfA)>0$ and $det(mathbfB)=0$, but $det(mathbfA+mathbfB)=(-1)cdot 2-4cdot 4=-18<0$.
edited Sep 6 at 11:26
answered Sep 6 at 11:08
cansomeonehelpmeout
5,5573830
5,5573830
Thanks. Umm actually $B$ was also a symmetric matrix. Is that okay to change the question?
â kayak
Sep 6 at 11:11
@kayak Sure! I'll delete my answer then, and think some more.
â cansomeonehelpmeout
Sep 6 at 11:12
1
As a guide for the future: Editing the question after someone's provided an answer is generally frowned upon, for it makes the original answer look silly, when the real silliness was in being sloppy about asking the question.
â John Hughes
Sep 6 at 12:03
@JohnHughes Oh sorry. Ill keep that in mind.
â kayak
Sep 7 at 4:25
add a comment |Â
Thanks. Umm actually $B$ was also a symmetric matrix. Is that okay to change the question?
â kayak
Sep 6 at 11:11
@kayak Sure! I'll delete my answer then, and think some more.
â cansomeonehelpmeout
Sep 6 at 11:12
1
As a guide for the future: Editing the question after someone's provided an answer is generally frowned upon, for it makes the original answer look silly, when the real silliness was in being sloppy about asking the question.
â John Hughes
Sep 6 at 12:03
@JohnHughes Oh sorry. Ill keep that in mind.
â kayak
Sep 7 at 4:25
Thanks. Umm actually $B$ was also a symmetric matrix. Is that okay to change the question?
â kayak
Sep 6 at 11:11
Thanks. Umm actually $B$ was also a symmetric matrix. Is that okay to change the question?
â kayak
Sep 6 at 11:11
@kayak Sure! I'll delete my answer then, and think some more.
â cansomeonehelpmeout
Sep 6 at 11:12
@kayak Sure! I'll delete my answer then, and think some more.
â cansomeonehelpmeout
Sep 6 at 11:12
1
1
As a guide for the future: Editing the question after someone's provided an answer is generally frowned upon, for it makes the original answer look silly, when the real silliness was in being sloppy about asking the question.
â John Hughes
Sep 6 at 12:03
As a guide for the future: Editing the question after someone's provided an answer is generally frowned upon, for it makes the original answer look silly, when the real silliness was in being sloppy about asking the question.
â John Hughes
Sep 6 at 12:03
@JohnHughes Oh sorry. Ill keep that in mind.
â kayak
Sep 7 at 4:25
@JohnHughes Oh sorry. Ill keep that in mind.
â kayak
Sep 7 at 4:25
add a comment |Â
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1
Not sure.. What about A = diag(1,1), B= diag(-1,0)?
â James
Sep 6 at 11:19