Question about determinants [on hold]

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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.

asked 3 hours ago

user176061

New contributor

put on hold as off-topic by Andrew, David Carlisle, Loop Space, Circumscribe, Kurt 3 hours ago

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
3 hours ago

Perhaps this should be migrated to math.stackexchange.com. I believe that the use of mathbb is not concise.
– CampanIgnis
3 hours ago

2

Homework questions generally remain unanswered on stack exchange, especially when they are posted on sites that are not directly relevant to them.
– Andrew
3 hours ago

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.

asked 3 hours ago

user176061

New contributor

put on hold as off-topic by Andrew, David Carlisle, Loop Space, Circumscribe, Kurt 3 hours ago

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
3 hours ago

Perhaps this should be migrated to math.stackexchange.com. I believe that the use of mathbb is not concise.
– CampanIgnis
3 hours ago

2

Homework questions generally remain unanswered on stack exchange, especially when they are posted on sites that are not directly relevant to them.
– Andrew
3 hours ago

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.

asked 3 hours ago

user176061

New contributor

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 3 hours ago

user176061

New contributor

asked 3 hours ago

user176061

New contributor

asked 3 hours ago

user176061

New contributor

asked 3 hours ago

user176061

asked 3 hours ago

user176061

New contributor

user176061 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

put on hold as off-topic by Andrew, David Carlisle, Loop Space, Circumscribe, Kurt 3 hours ago

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.

put on hold as off-topic by Andrew, David Carlisle, Loop Space, Circumscribe, Kurt 3 hours ago

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
3 hours ago

Perhaps this should be migrated to math.stackexchange.com. I believe that the use of mathbb is not concise.
– CampanIgnis
3 hours ago

2

Homework questions generally remain unanswered on stack exchange, especially when they are posted on sites that are not directly relevant to them.
– Andrew
3 hours ago

add a comment |

3

Are you sure you're on the relevant site?
– Bernard
3 hours ago

Perhaps this should be migrated to math.stackexchange.com. I believe that the use of mathbb is not concise.
– CampanIgnis
3 hours ago

2

Homework questions generally remain unanswered on stack exchange, especially when they are posted on sites that are not directly relevant to them.
– Andrew
3 hours ago

Are you sure you're on the relevant site?
– Bernard
3 hours ago

Perhaps this should be migrated to math.stackexchange.com. I believe that the use of mathbb is not concise.
– CampanIgnis
3 hours ago

Homework questions generally remain unanswered on stack exchange, especially when they are posted on sites that are not directly relevant to them.
– Andrew
3 hours ago

add a comment |

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