Known conditions to make $A otimes B$ be pos.def., even if $A$ is not pos.def.?
up vote
0
down vote
favorite
Are there conditions that I should demand to be sure that $A otimes B$ is positive definite, even when allowing $A$ not being positive definite, while $B$ is positive definite?
linear-algebra matrices tensor-products positive-definite
asked Nov 17 at 16:54
An old man in the sea.
1,60411031
add a comment |
up vote
0
down vote
favorite
Are there conditions that I should demand to be sure that $A otimes B$ is positive definite, even when allowing $A$ not being positive definite, while $B$ is positive definite?
linear-algebra matrices tensor-products positive-definite
asked Nov 17 at 16:54
An old man in the sea.
1,60411031
1
I suppose $A$ and $B$ could both be negative definite.
– Lord Shark the Unknown
Nov 17 at 17:12
@LordSharktheUnknown Thanks for the comment. I forgot the $B$ matrix must be pos.def. , and edited the question accordingly. I'm sorry for my error,.
– An old man in the sea.
Nov 17 at 17:14
1
In this context, does positive definite mean symmetric?
– Omnomnomnom
Nov 17 at 23:45
Assuming positive definite means symmetric here: If $B$ is positive definite, then $A otimes B$ will be positive definite if and only if $A$ is also positive definite.
– Omnomnomnom
Nov 17 at 23:47
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Are there conditions that I should demand to be sure that $A otimes B$ is positive definite, even when allowing $A$ not being positive definite, while $B$ is positive definite?
linear-algebra matrices tensor-products positive-definite
asked Nov 17 at 16:54
An old man in the sea.
1,60411031
Are there conditions that I should demand to be sure that $A otimes B$ is positive definite, even when allowing $A$ not being positive definite, while $B$ is positive definite?
linear-algebra matrices tensor-products positive-definite
linear-algebra matrices tensor-products positive-definite
asked Nov 17 at 16:54
An old man in the sea.
1,60411031
asked Nov 17 at 16:54
An old man in the sea.
1,60411031
edited Nov 17 at 17:13
asked Nov 17 at 16:54
An old man in the sea.
1,60411031
asked Nov 17 at 16:54
An old man in the sea.
1,60411031
asked Nov 17 at 16:54
An old man in the sea.
1,60411031
1,60411031
1
I suppose $A$ and $B$ could both be negative definite.
– Lord Shark the Unknown
Nov 17 at 17:12
@LordSharktheUnknown Thanks for the comment. I forgot the $B$ matrix must be pos.def. , and edited the question accordingly. I'm sorry for my error,.
– An old man in the sea.
Nov 17 at 17:14
1
In this context, does positive definite mean symmetric?
– Omnomnomnom
Nov 17 at 23:45
Assuming positive definite means symmetric here: If $B$ is positive definite, then $A otimes B$ will be positive definite if and only if $A$ is also positive definite.
– Omnomnomnom
Nov 17 at 23:47
add a comment |
1
I suppose $A$ and $B$ could both be negative definite.
– Lord Shark the Unknown
Nov 17 at 17:12
@LordSharktheUnknown Thanks for the comment. I forgot the $B$ matrix must be pos.def. , and edited the question accordingly. I'm sorry for my error,.
– An old man in the sea.
Nov 17 at 17:14
1
In this context, does positive definite mean symmetric?
– Omnomnomnom
Nov 17 at 23:45
Assuming positive definite means symmetric here: If $B$ is positive definite, then $A otimes B$ will be positive definite if and only if $A$ is also positive definite.
– Omnomnomnom
Nov 17 at 23:47
1
1
I suppose $A$ and $B$ could both be negative definite.
– Lord Shark the Unknown
Nov 17 at 17:12
I suppose $A$ and $B$ could both be negative definite.
– Lord Shark the Unknown
Nov 17 at 17:12
@LordSharktheUnknown Thanks for the comment. I forgot the $B$ matrix must be pos.def. , and edited the question accordingly. I'm sorry for my error,.
– An old man in the sea.
Nov 17 at 17:14
@LordSharktheUnknown Thanks for the comment. I forgot the $B$ matrix must be pos.def. , and edited the question accordingly. I'm sorry for my error,.
– An old man in the sea.
Nov 17 at 17:14
1
1
In this context, does positive definite mean symmetric?
– Omnomnomnom
Nov 17 at 23:45
In this context, does positive definite mean symmetric?
– Omnomnomnom
Nov 17 at 23:45
Assuming positive definite means symmetric here: If $B$ is positive definite, then $A otimes B$ will be positive definite if and only if $A$ is also positive definite.
– Omnomnomnom
Nov 17 at 23:47
Assuming positive definite means symmetric here: If $B$ is positive definite, then $A otimes B$ will be positive definite if and only if $A$ is also positive definite.
– Omnomnomnom
Nov 17 at 23:47
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
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.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- 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.
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%2f3002569%2fknown-conditions-to-make-a-otimes-b-be-pos-def-even-if-a-is-not-pos-def%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
1
I suppose $A$ and $B$ could both be negative definite.
– Lord Shark the Unknown
Nov 17 at 17:12
@LordSharktheUnknown Thanks for the comment. I forgot the $B$ matrix must be pos.def. , and edited the question accordingly. I'm sorry for my error,.
– An old man in the sea.
Nov 17 at 17:14
1
In this context, does positive definite mean symmetric?
– Omnomnomnom
Nov 17 at 23:45
Assuming positive definite means symmetric here: If $B$ is positive definite, then $A otimes B$ will be positive definite if and only if $A$ is also positive definite.
– Omnomnomnom
Nov 17 at 23:47