The distance of $y$ from $A$ equals $||y-overline y||$?
Is the following true in $Bbb R^n$?
If $A$ is a one-dimensional subspace spanned by $u$ then for any vector $yin Bbb R^n$ the distance of $y$ from $A$ equals $||y-overline y||$
where $overline y$ is the othogonal projection of $y$ on $u$.
I know that the othogonal projection of $y$ on $u$ is $ y=frac{langle y,urangle }{langle u,urangle } u$
Also $y-overline y$ is orthogonal to $u$.
I have proved these.
But how to prove or disprove the above ?Please help
linear-algebra geometry
asked Nov 29 at 15:00
Join_PhD
1968
add a comment |
Is the following true in $Bbb R^n$?
If $A$ is a one-dimensional subspace spanned by $u$ then for any vector $yin Bbb R^n$ the distance of $y$ from $A$ equals $||y-overline y||$
where $overline y$ is the othogonal projection of $y$ on $u$.
I know that the othogonal projection of $y$ on $u$ is $ y=frac{langle y,urangle }{langle u,urangle } u$
Also $y-overline y$ is orthogonal to $u$.
I have proved these.
But how to prove or disprove the above ?Please help
linear-algebra geometry
asked Nov 29 at 15:00
Join_PhD
1968
add a comment |
Is the following true in $Bbb R^n$?
If $A$ is a one-dimensional subspace spanned by $u$ then for any vector $yin Bbb R^n$ the distance of $y$ from $A$ equals $||y-overline y||$
where $overline y$ is the othogonal projection of $y$ on $u$.
I know that the othogonal projection of $y$ on $u$ is $ y=frac{langle y,urangle }{langle u,urangle } u$
Also $y-overline y$ is orthogonal to $u$.
I have proved these.
But how to prove or disprove the above ?Please help
linear-algebra geometry
asked Nov 29 at 15:00
Join_PhD
1968
Is the following true in $Bbb R^n$?
If $A$ is a one-dimensional subspace spanned by $u$ then for any vector $yin Bbb R^n$ the distance of $y$ from $A$ equals $||y-overline y||$
where $overline y$ is the othogonal projection of $y$ on $u$.
I know that the othogonal projection of $y$ on $u$ is $ y=frac{langle y,urangle }{langle u,urangle } u$
Also $y-overline y$ is orthogonal to $u$.
I have proved these.
But how to prove or disprove the above ?Please help
linear-algebra geometry
linear-algebra geometry
asked Nov 29 at 15:00
Join_PhD
1968
asked Nov 29 at 15:00
Join_PhD
1968
asked Nov 29 at 15:00
Join_PhD
1968
asked Nov 29 at 15:00
Join_PhD
1968
asked Nov 29 at 15:00
Join_PhD
1968
1968
add a comment |
add a comment |
1 Answer
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Hint: For any $xin A$, we have $|y-x|^2 =|y-bar y|^2+|bar y-x|^2$.
answered Nov 29 at 15:18
Berci
59.4k23672
add a comment |
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1 Answer
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Hint: For any $xin A$, we have $|y-x|^2 =|y-bar y|^2+|bar y-x|^2$.
answered Nov 29 at 15:18
Berci
59.4k23672
add a comment |
Hint: For any $xin A$, we have $|y-x|^2 =|y-bar y|^2+|bar y-x|^2$.
answered Nov 29 at 15:18
Berci
59.4k23672
add a comment |
Hint: For any $xin A$, we have $|y-x|^2 =|y-bar y|^2+|bar y-x|^2$.
answered Nov 29 at 15:18
Berci
59.4k23672
Hint: For any $xin A$, we have $|y-x|^2 =|y-bar y|^2+|bar y-x|^2$.
answered Nov 29 at 15:18
Berci
59.4k23672
answered Nov 29 at 15:18
Berci
59.4k23672
answered Nov 29 at 15:18
Berci
59.4k23672
answered Nov 29 at 15:18
Berci
59.4k23672
59.4k23672
add a comment |
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