Question about determinants [closed]
up vote
0
down vote
favorite
Let $A,B in mathbb{M}_{nxn}(mathbb{R})$ be square matrices with real coefficients, and consider the function
$$ f(t)=det(mathbb{A}+tmathbb{B})
$$
Show that $mathbb{f}$ is a polynomial in $mathbb{t}$, and that for invertible $mathbb{A}$ the derivative at t=0 given by
$$ f'(0)=det(mathbb{A})tr(mathbb{A}^{-1}{B})$$
where tr is the trace.
matrices
asked Dec 3 at 20:57
user176061
1
closed as off-topic by Andrew, David Carlisle, Loop Space, Circumscribe, Kurt Dec 3 at 21:42
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question does not fall within the scope of TeX, LaTeX or related typesetting systems as defined in the help center." – Andrew, David Carlisle, Loop Space, Circumscribe, Kurt
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
up vote
0
down vote
favorite
Let $A,B in mathbb{M}_{nxn}(mathbb{R})$ be square matrices with real coefficients, and consider the function
$$ f(t)=det(mathbb{A}+tmathbb{B})
$$
Show that $mathbb{f}$ is a polynomial in $mathbb{t}$, and that for invertible $mathbb{A}$ the derivative at t=0 given by
$$ f'(0)=det(mathbb{A})tr(mathbb{A}^{-1}{B})$$
where tr is the trace.
matrices
asked Dec 3 at 20:57
user176061
1
closed as off-topic by Andrew, David Carlisle, Loop Space, Circumscribe, Kurt Dec 3 at 21:42
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question does not fall within the scope of TeX, LaTeX or related typesetting systems as defined in the help center." – Andrew, David Carlisle, Loop Space, Circumscribe, Kurt
If this question can be reworded to fit the rules in the help center, please edit the question.
3
Are you sure you're on the relevant site?
– Bernard
Dec 3 at 20:59
Perhaps this should be migrated to math.stackexchange.com. I believe that the use ofmathbbis not concise.
– CampanIgnis
Dec 3 at 21:00
2
Homework questions generally remain unanswered on stack exchange, especially when they are posted on sites that are not directly relevant to them.
– Andrew
Dec 3 at 21:10
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Let $A,B in mathbb{M}_{nxn}(mathbb{R})$ be square matrices with real coefficients, and consider the function
$$ f(t)=det(mathbb{A}+tmathbb{B})
$$
Show that $mathbb{f}$ is a polynomial in $mathbb{t}$, and that for invertible $mathbb{A}$ the derivative at t=0 given by
$$ f'(0)=det(mathbb{A})tr(mathbb{A}^{-1}{B})$$
where tr is the trace.
matrices
asked Dec 3 at 20:57
user176061
1
Let $A,B in mathbb{M}_{nxn}(mathbb{R})$ be square matrices with real coefficients, and consider the function
$$ f(t)=det(mathbb{A}+tmathbb{B})
$$
Show that $mathbb{f}$ is a polynomial in $mathbb{t}$, and that for invertible $mathbb{A}$ the derivative at t=0 given by
$$ f'(0)=det(mathbb{A})tr(mathbb{A}^{-1}{B})$$
where tr is the trace.
matrices
matrices
asked Dec 3 at 20:57
user176061
1
asked Dec 3 at 20:57
user176061
1
asked Dec 3 at 20:57
user176061
1
asked Dec 3 at 20:57
user176061
1
asked Dec 3 at 20:57
user176061
1
1
closed as off-topic by Andrew, David Carlisle, Loop Space, Circumscribe, Kurt Dec 3 at 21:42
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question does not fall within the scope of TeX, LaTeX or related typesetting systems as defined in the help center." – Andrew, David Carlisle, Loop Space, Circumscribe, Kurt
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Andrew, David Carlisle, Loop Space, Circumscribe, Kurt Dec 3 at 21:42
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question does not fall within the scope of TeX, LaTeX or related typesetting systems as defined in the help center." – Andrew, David Carlisle, Loop Space, Circumscribe, Kurt
If this question can be reworded to fit the rules in the help center, please edit the question.
3
Are you sure you're on the relevant site?
– Bernard
Dec 3 at 20:59
Perhaps this should be migrated to math.stackexchange.com. I believe that the use ofmathbbis not concise.
– CampanIgnis
Dec 3 at 21:00
2
Homework questions generally remain unanswered on stack exchange, especially when they are posted on sites that are not directly relevant to them.
– Andrew
Dec 3 at 21:10
add a comment |
3
Are you sure you're on the relevant site?
– Bernard
Dec 3 at 20:59
Perhaps this should be migrated to math.stackexchange.com. I believe that the use ofmathbbis not concise.
– CampanIgnis
Dec 3 at 21:00
2
Homework questions generally remain unanswered on stack exchange, especially when they are posted on sites that are not directly relevant to them.
– Andrew
Dec 3 at 21:10
3
3
Are you sure you're on the relevant site?
– Bernard
Dec 3 at 20:59
Are you sure you're on the relevant site?
– Bernard
Dec 3 at 20:59
Perhaps this should be migrated to math.stackexchange.com. I believe that the use of
mathbb is not concise.– CampanIgnis
Dec 3 at 21:00
Perhaps this should be migrated to math.stackexchange.com. I believe that the use of
mathbb is not concise.– CampanIgnis
Dec 3 at 21:00
2
2
Homework questions generally remain unanswered on stack exchange, especially when they are posted on sites that are not directly relevant to them.
– Andrew
Dec 3 at 21:10
Homework questions generally remain unanswered on stack exchange, especially when they are posted on sites that are not directly relevant to them.
– Andrew
Dec 3 at 21:10
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
3
Are you sure you're on the relevant site?
– Bernard
Dec 3 at 20:59
Perhaps this should be migrated to math.stackexchange.com. I believe that the use of
mathbbis not concise.– CampanIgnis
Dec 3 at 21:00
2
Homework questions generally remain unanswered on stack exchange, especially when they are posted on sites that are not directly relevant to them.
– Andrew
Dec 3 at 21:10