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.










share|improve this 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 of mathbb is 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















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.










share|improve this 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 of mathbb is 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













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.










share|improve this question













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






share|improve this question













share|improve this question











share|improve this question




share|improve this question










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 of mathbb is 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




    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








  • 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















active

oldest

votes






















active

oldest

votes













active

oldest

votes









active

oldest

votes






active

oldest

votes

Popular posts from this blog

mysqli_query(): Empty query in /home/lucindabrummitt/public_html/blog/wp-includes/wp-db.php on line 1924

How to change which sound is reproduced for terminal bell?

Can I use Tabulator js library in my java Spring + Thymeleaf project?