Show that $U := { v ∈ Bbb R^n : ∀ u ∈ U : 〈 v , u 〉 = c } $ is an affine subspace
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Let $c∈Bbb R$ and $U⊂Bbb R^n$,$U ne∅$ ($U$ is a nonempty subset). Further let $〈·,·〉:Bbb R^n×Bbb R^n→Bbb R$ be the standard
inner product. Define
$$U := { v ∈ Bbb R^n : ∀ u ∈ U : 〈 v , u 〉 = c } .$$
Show that $Uc$ is an affine subspace.
I think I should use the Inner standard product.
Can someone help me to solve it ? how the begin should be?
linear-algebra affine-geometry
asked Nov 18 at 13:55
Amerov
35
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up vote
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down vote
favorite
Let $c∈Bbb R$ and $U⊂Bbb R^n$,$U ne∅$ ($U$ is a nonempty subset). Further let $〈·,·〉:Bbb R^n×Bbb R^n→Bbb R$ be the standard
inner product. Define
$$U := { v ∈ Bbb R^n : ∀ u ∈ U : 〈 v , u 〉 = c } .$$
Show that $Uc$ is an affine subspace.
I think I should use the Inner standard product.
Can someone help me to solve it ? how the begin should be?
linear-algebra affine-geometry
asked Nov 18 at 13:55
Amerov
35
Hint: A subset is an affine subspace if and only if it differs from a linear subspace by a constant.
– user3482749
Nov 18 at 13:59
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Let $c∈Bbb R$ and $U⊂Bbb R^n$,$U ne∅$ ($U$ is a nonempty subset). Further let $〈·,·〉:Bbb R^n×Bbb R^n→Bbb R$ be the standard
inner product. Define
$$U := { v ∈ Bbb R^n : ∀ u ∈ U : 〈 v , u 〉 = c } .$$
Show that $Uc$ is an affine subspace.
I think I should use the Inner standard product.
Can someone help me to solve it ? how the begin should be?
linear-algebra affine-geometry
asked Nov 18 at 13:55
Amerov
35
Let $c∈Bbb R$ and $U⊂Bbb R^n$,$U ne∅$ ($U$ is a nonempty subset). Further let $〈·,·〉:Bbb R^n×Bbb R^n→Bbb R$ be the standard
inner product. Define
$$U := { v ∈ Bbb R^n : ∀ u ∈ U : 〈 v , u 〉 = c } .$$
Show that $Uc$ is an affine subspace.
I think I should use the Inner standard product.
Can someone help me to solve it ? how the begin should be?
linear-algebra affine-geometry
linear-algebra affine-geometry
asked Nov 18 at 13:55
Amerov
35
asked Nov 18 at 13:55
Amerov
35
edited Nov 18 at 14:14
asked Nov 18 at 13:55
Amerov
35
asked Nov 18 at 13:55
Amerov
35
asked Nov 18 at 13:55
Amerov
35
35
Hint: A subset is an affine subspace if and only if it differs from a linear subspace by a constant.
– user3482749
Nov 18 at 13:59
add a comment |
Hint: A subset is an affine subspace if and only if it differs from a linear subspace by a constant.
– user3482749
Nov 18 at 13:59
Hint: A subset is an affine subspace if and only if it differs from a linear subspace by a constant.
– user3482749
Nov 18 at 13:59
Hint: A subset is an affine subspace if and only if it differs from a linear subspace by a constant.
– user3482749
Nov 18 at 13:59
add a comment |
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Hint: A subset is an affine subspace if and only if it differs from a linear subspace by a constant.
– user3482749
Nov 18 at 13:59