Mixing
Orthogonal projection of $v = (0,0,5,0)^T$ onto the subspace $W$.
To find the orthogonal projection of $v = (0,0,5,0)^T$ onto the subspace $W$ spanned by $(-1,-1,-1,1)^T,(-1,1,1,1)^T,(-1,-1,1,-1)^T$.
Since the vectors which forms a basis for $W$ are already orthogonal, the orthogonal projection of $v = (0,0,5,0)^T$ onto the subspace $W$ is the sum of the projection of $v$ on each of the basis vectors.
Is my logic and method correct?
linear-algebra matrices vector-spaces
asked Nov 20 '18 at 12:05
user8795
5,61961947
add a comment |
To find the orthogonal projection of $v = (0,0,5,0)^T$ onto the subspace $W$ spanned by $(-1,-1,-1,1)^T,(-1,1,1,1)^T,(-1,-1,1,-1)^T$.
Since the vectors which forms a basis for $W$ are already orthogonal, the orthogonal projection of $v = (0,0,5,0)^T$ onto the subspace $W$ is the sum of the projection of $v$ on each of the basis vectors.
Is my logic and method correct?
linear-algebra matrices vector-spaces
asked Nov 20 '18 at 12:05
user8795
5,61961947
add a comment |
To find the orthogonal projection of $v = (0,0,5,0)^T$ onto the subspace $W$ spanned by $(-1,-1,-1,1)^T,(-1,1,1,1)^T,(-1,-1,1,-1)^T$.
Since the vectors which forms a basis for $W$ are already orthogonal, the orthogonal projection of $v = (0,0,5,0)^T$ onto the subspace $W$ is the sum of the projection of $v$ on each of the basis vectors.
Is my logic and method correct?
linear-algebra matrices vector-spaces
asked Nov 20 '18 at 12:05
user8795
5,61961947
To find the orthogonal projection of $v = (0,0,5,0)^T$ onto the subspace $W$ spanned by $(-1,-1,-1,1)^T,(-1,1,1,1)^T,(-1,-1,1,-1)^T$.
Since the vectors which forms a basis for $W$ are already orthogonal, the orthogonal projection of $v = (0,0,5,0)^T$ onto the subspace $W$ is the sum of the projection of $v$ on each of the basis vectors.
Is my logic and method correct?
linear-algebra matrices vector-spaces
linear-algebra matrices vector-spaces
asked Nov 20 '18 at 12:05
user8795
5,61961947
asked Nov 20 '18 at 12:05
user8795
5,61961947
asked Nov 20 '18 at 12:05
user8795
5,61961947
asked Nov 20 '18 at 12:05
user8795
5,61961947
asked Nov 20 '18 at 12:05
user8795
5,61961947
5,61961947
add a comment |
add a comment |
1 Answer
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Yes, it's fine assuming that by projection of $v$ on a a vector $w$ you mean $frac{langle v,wrangle}{lVert wrVert|^2}w$.
answered Nov 20 '18 at 12:09
José Carlos Santos
150k22121221
add a comment |
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1 Answer
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1 Answer
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active
oldest
votes
Yes, it's fine assuming that by projection of $v$ on a a vector $w$ you mean $frac{langle v,wrangle}{lVert wrVert|^2}w$.
answered Nov 20 '18 at 12:09
José Carlos Santos
150k22121221
add a comment |
Yes, it's fine assuming that by projection of $v$ on a a vector $w$ you mean $frac{langle v,wrangle}{lVert wrVert|^2}w$.
answered Nov 20 '18 at 12:09
José Carlos Santos
150k22121221
add a comment |
Yes, it's fine assuming that by projection of $v$ on a a vector $w$ you mean $frac{langle v,wrangle}{lVert wrVert|^2}w$.
answered Nov 20 '18 at 12:09
José Carlos Santos
150k22121221
Yes, it's fine assuming that by projection of $v$ on a a vector $w$ you mean $frac{langle v,wrangle}{lVert wrVert|^2}w$.
answered Nov 20 '18 at 12:09
José Carlos Santos
150k22121221
answered Nov 20 '18 at 12:09
José Carlos Santos
150k22121221
answered Nov 20 '18 at 12:09
José Carlos Santos
150k22121221
answered Nov 20 '18 at 12:09
José Carlos Santos
150k22121221
150k22121221
add a comment |
add a comment |
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