A question about a polynomial characteristic of a square matrix [closed]
There is a theorem in linear algebra where we have the following equality
$x^{n}=left ( x-1 right )^{2}pleft ( x right )+nx+left ( 1-n right )$,
$pleft ( x right )$ is the characteristic polynomial of a square matrix $A$ of order $n$
Thanks for your help.
linear-algebra
asked Dec 27 '18 at 7:30
Victor Huuanca Sullca
1523
closed as unclear what you're asking by Davide Giraudo, Eric Wofsey, mrtaurho, Eevee Trainer, Lord Shark the Unknown Dec 28 '18 at 2:49
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
There is a theorem in linear algebra where we have the following equality
$x^{n}=left ( x-1 right )^{2}pleft ( x right )+nx+left ( 1-n right )$,
$pleft ( x right )$ is the characteristic polynomial of a square matrix $A$ of order $n$
Thanks for your help.
linear-algebra
asked Dec 27 '18 at 7:30
Victor Huuanca Sullca
1523
closed as unclear what you're asking by Davide Giraudo, Eric Wofsey, mrtaurho, Eevee Trainer, Lord Shark the Unknown Dec 28 '18 at 2:49
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
I am not sure what your question is, but if you set $y=(x-1)$ so that $x^n=(y+1)^n$ you can use the binomial expansion to show that the equality is true.
– Mark Bennet
Dec 27 '18 at 7:38
2
It can not be true, because LHS is polinomial of degree n wheras the RHS is polinomial of degree n+2
– Minz
Dec 27 '18 at 8:45
add a comment |
There is a theorem in linear algebra where we have the following equality
$x^{n}=left ( x-1 right )^{2}pleft ( x right )+nx+left ( 1-n right )$,
$pleft ( x right )$ is the characteristic polynomial of a square matrix $A$ of order $n$
Thanks for your help.
linear-algebra
asked Dec 27 '18 at 7:30
Victor Huuanca Sullca
1523
There is a theorem in linear algebra where we have the following equality
$x^{n}=left ( x-1 right )^{2}pleft ( x right )+nx+left ( 1-n right )$,
$pleft ( x right )$ is the characteristic polynomial of a square matrix $A$ of order $n$
Thanks for your help.
linear-algebra
linear-algebra
asked Dec 27 '18 at 7:30
Victor Huuanca Sullca
1523
asked Dec 27 '18 at 7:30
Victor Huuanca Sullca
1523
asked Dec 27 '18 at 7:30
Victor Huuanca Sullca
1523
asked Dec 27 '18 at 7:30
Victor Huuanca Sullca
1523
asked Dec 27 '18 at 7:30
Victor Huuanca Sullca
1523
1523
closed as unclear what you're asking by Davide Giraudo, Eric Wofsey, mrtaurho, Eevee Trainer, Lord Shark the Unknown Dec 28 '18 at 2:49
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as unclear what you're asking by Davide Giraudo, Eric Wofsey, mrtaurho, Eevee Trainer, Lord Shark the Unknown Dec 28 '18 at 2:49
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
I am not sure what your question is, but if you set $y=(x-1)$ so that $x^n=(y+1)^n$ you can use the binomial expansion to show that the equality is true.
– Mark Bennet
Dec 27 '18 at 7:38
2
It can not be true, because LHS is polinomial of degree n wheras the RHS is polinomial of degree n+2
– Minz
Dec 27 '18 at 8:45
add a comment |
I am not sure what your question is, but if you set $y=(x-1)$ so that $x^n=(y+1)^n$ you can use the binomial expansion to show that the equality is true.
– Mark Bennet
Dec 27 '18 at 7:38
2
It can not be true, because LHS is polinomial of degree n wheras the RHS is polinomial of degree n+2
– Minz
Dec 27 '18 at 8:45
I am not sure what your question is, but if you set $y=(x-1)$ so that $x^n=(y+1)^n$ you can use the binomial expansion to show that the equality is true.
– Mark Bennet
Dec 27 '18 at 7:38
I am not sure what your question is, but if you set $y=(x-1)$ so that $x^n=(y+1)^n$ you can use the binomial expansion to show that the equality is true.
– Mark Bennet
Dec 27 '18 at 7:38
2
2
It can not be true, because LHS is polinomial of degree n wheras the RHS is polinomial of degree n+2
– Minz
Dec 27 '18 at 8:45
It can not be true, because LHS is polinomial of degree n wheras the RHS is polinomial of degree n+2
– Minz
Dec 27 '18 at 8:45
add a comment |
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I am not sure what your question is, but if you set $y=(x-1)$ so that $x^n=(y+1)^n$ you can use the binomial expansion to show that the equality is true.
– Mark Bennet
Dec 27 '18 at 7:38
2
It can not be true, because LHS is polinomial of degree n wheras the RHS is polinomial of degree n+2
– Minz
Dec 27 '18 at 8:45