Let $T: Bbb R^n to Bbb R^n$ be a linear transformation which satisfies $T^2(v)=-v$ for all $vinBbb R^n$ then...
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Let $T: Bbb R^n to Bbb R^n$ be a linear transformation which satisfies $T^2(v)=-v$ for all $vinBbb R^n$ then $n$ is always even?
abstract-algebra
edited Nov 23 at 15:37
David C. Ullrich
57.3k43791
asked Nov 23 at 15:30
Muskan khanam
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up vote
-2
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Let $T: Bbb R^n to Bbb R^n$ be a linear transformation which satisfies $T^2(v)=-v$ for all $vinBbb R^n$ then $n$ is always even?
abstract-algebra
edited Nov 23 at 15:37
David C. Ullrich
57.3k43791
asked Nov 23 at 15:30
Muskan khanam
1
add a comment |
up vote
-2
down vote
favorite
up vote
-2
down vote
favorite
Let $T: Bbb R^n to Bbb R^n$ be a linear transformation which satisfies $T^2(v)=-v$ for all $vinBbb R^n$ then $n$ is always even?
abstract-algebra
edited Nov 23 at 15:37
David C. Ullrich
57.3k43791
asked Nov 23 at 15:30
Muskan khanam
1
Let $T: Bbb R^n to Bbb R^n$ be a linear transformation which satisfies $T^2(v)=-v$ for all $vinBbb R^n$ then $n$ is always even?
abstract-algebra
abstract-algebra
edited Nov 23 at 15:37
David C. Ullrich
57.3k43791
asked Nov 23 at 15:30
Muskan khanam
1
edited Nov 23 at 15:37
David C. Ullrich
57.3k43791
asked Nov 23 at 15:30
Muskan khanam
1
edited Nov 23 at 15:37
David C. Ullrich
57.3k43791
edited Nov 23 at 15:37
David C. Ullrich
57.3k43791
edited Nov 23 at 15:37
David C. Ullrich
57.3k43791
57.3k43791
asked Nov 23 at 15:30
Muskan khanam
1
asked Nov 23 at 15:30
Muskan khanam
1
asked Nov 23 at 15:30
Muskan khanam
1
1
add a comment |
add a comment |
1 Answer
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Yes. Hint: If $p$ is a polynomial with real coefficients and $p$ has odd degree then there exists $xinBbb R$ with $p(x)=0$.
answered Nov 23 at 15:39
David C. Ullrich
57.3k43791
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
-1
down vote
Yes. Hint: If $p$ is a polynomial with real coefficients and $p$ has odd degree then there exists $xinBbb R$ with $p(x)=0$.
answered Nov 23 at 15:39
David C. Ullrich
57.3k43791
add a comment |
up vote
-1
down vote
Yes. Hint: If $p$ is a polynomial with real coefficients and $p$ has odd degree then there exists $xinBbb R$ with $p(x)=0$.
answered Nov 23 at 15:39
David C. Ullrich
57.3k43791
add a comment |
up vote
-1
down vote
up vote
-1
down vote
Yes. Hint: If $p$ is a polynomial with real coefficients and $p$ has odd degree then there exists $xinBbb R$ with $p(x)=0$.
answered Nov 23 at 15:39
David C. Ullrich
57.3k43791
Yes. Hint: If $p$ is a polynomial with real coefficients and $p$ has odd degree then there exists $xinBbb R$ with $p(x)=0$.
answered Nov 23 at 15:39
David C. Ullrich
57.3k43791
answered Nov 23 at 15:39
David C. Ullrich
57.3k43791
answered Nov 23 at 15:39
David C. Ullrich
57.3k43791
answered Nov 23 at 15:39
David C. Ullrich
57.3k43791
57.3k43791
add a comment |
add a comment |
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