Mixing
orthogonal function and inner product space
$begingroup$
Consider the inner product space $$langle f,g rangle= int_{-1}^{1} f(x) g(x) dx $$
find the non zero orthogonal function with respect to $f(x)=1$ in the subspace span of ${1,e^{x}}$ ?
inner-product-space
edited Jan 31 at 19:28
Ahmad Bazzi
8,4912824
asked Jan 31 at 19:23
Allic MendoncaAllic Mendonca
12
$endgroup$
add a comment |
$begingroup$
Consider the inner product space $$langle f,g rangle= int_{-1}^{1} f(x) g(x) dx $$
find the non zero orthogonal function with respect to $f(x)=1$ in the subspace span of ${1,e^{x}}$ ?
inner-product-space
edited Jan 31 at 19:28
Ahmad Bazzi
8,4912824
asked Jan 31 at 19:23
Allic MendoncaAllic Mendonca
12
$endgroup$
$begingroup$
hi please use LaTeX as I did right now. Also please make sure the notation corresponds to your true question.
$endgroup$
– Ahmad Bazzi
Jan 31 at 19:26
$begingroup$
-1 to 1 is the interval. can you add it too?
$endgroup$
– Allic Mendonca
Jan 31 at 19:27
add a comment |
$begingroup$
Consider the inner product space $$langle f,g rangle= int_{-1}^{1} f(x) g(x) dx $$
find the non zero orthogonal function with respect to $f(x)=1$ in the subspace span of ${1,e^{x}}$ ?
inner-product-space
edited Jan 31 at 19:28
Ahmad Bazzi
8,4912824
asked Jan 31 at 19:23
Allic MendoncaAllic Mendonca
12
$endgroup$
Consider the inner product space $$langle f,g rangle= int_{-1}^{1} f(x) g(x) dx $$
find the non zero orthogonal function with respect to $f(x)=1$ in the subspace span of ${1,e^{x}}$ ?
inner-product-space
inner-product-space
edited Jan 31 at 19:28
Ahmad Bazzi
8,4912824
asked Jan 31 at 19:23
Allic MendoncaAllic Mendonca
12
edited Jan 31 at 19:28
Ahmad Bazzi
8,4912824
asked Jan 31 at 19:23
Allic MendoncaAllic Mendonca
12
edited Jan 31 at 19:28
Ahmad Bazzi
8,4912824
edited Jan 31 at 19:28
Ahmad Bazzi
8,4912824
edited Jan 31 at 19:28
Ahmad Bazzi
8,4912824
8,4912824
asked Jan 31 at 19:23
Allic MendoncaAllic Mendonca
12
asked Jan 31 at 19:23
Allic MendoncaAllic Mendonca
12
asked Jan 31 at 19:23
Allic MendoncaAllic Mendonca
12
12
$begingroup$
hi please use LaTeX as I did right now. Also please make sure the notation corresponds to your true question.
$endgroup$
– Ahmad Bazzi
Jan 31 at 19:26
$begingroup$
-1 to 1 is the interval. can you add it too?
$endgroup$
– Allic Mendonca
Jan 31 at 19:27
add a comment |
$begingroup$
hi please use LaTeX as I did right now. Also please make sure the notation corresponds to your true question.
$endgroup$
– Ahmad Bazzi
Jan 31 at 19:26
$begingroup$
-1 to 1 is the interval. can you add it too?
$endgroup$
– Allic Mendonca
Jan 31 at 19:27
$begingroup$
hi please use LaTeX as I did right now. Also please make sure the notation corresponds to your true question.
$endgroup$
– Ahmad Bazzi
Jan 31 at 19:26
$begingroup$
hi please use LaTeX as I did right now. Also please make sure the notation corresponds to your true question.
$endgroup$
– Ahmad Bazzi
Jan 31 at 19:26
$begingroup$
-1 to 1 is the interval. can you add it too?
$endgroup$
– Allic Mendonca
Jan 31 at 19:27
$begingroup$
-1 to 1 is the interval. can you add it too?
$endgroup$
– Allic Mendonca
Jan 31 at 19:27
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
If you compute the orthogonal projektion $P(e^x)$ on span(1). Then $e^x - P(e^x)$ is in the orthogonal complement of span(1).
answered Jan 31 at 19:35
Leander Tilsted KristensenLeander Tilsted Kristensen
664
$endgroup$
add a comment |
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1 Answer
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active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
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active
oldest
votes
$begingroup$
If you compute the orthogonal projektion $P(e^x)$ on span(1). Then $e^x - P(e^x)$ is in the orthogonal complement of span(1).
answered Jan 31 at 19:35
Leander Tilsted KristensenLeander Tilsted Kristensen
664
$endgroup$
add a comment |
$begingroup$
If you compute the orthogonal projektion $P(e^x)$ on span(1). Then $e^x - P(e^x)$ is in the orthogonal complement of span(1).
answered Jan 31 at 19:35
Leander Tilsted KristensenLeander Tilsted Kristensen
664
$endgroup$
add a comment |
$begingroup$
If you compute the orthogonal projektion $P(e^x)$ on span(1). Then $e^x - P(e^x)$ is in the orthogonal complement of span(1).
answered Jan 31 at 19:35
Leander Tilsted KristensenLeander Tilsted Kristensen
664
$endgroup$
If you compute the orthogonal projektion $P(e^x)$ on span(1). Then $e^x - P(e^x)$ is in the orthogonal complement of span(1).
answered Jan 31 at 19:35
Leander Tilsted KristensenLeander Tilsted Kristensen
664
answered Jan 31 at 19:35
Leander Tilsted KristensenLeander Tilsted Kristensen
664
answered Jan 31 at 19:35
Leander Tilsted KristensenLeander Tilsted Kristensen
664
answered Jan 31 at 19:35
Leander Tilsted KristensenLeander Tilsted Kristensen
664
664
add a comment |
add a comment |
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$begingroup$
hi please use LaTeX as I did right now. Also please make sure the notation corresponds to your true question.
$endgroup$
– Ahmad Bazzi
Jan 31 at 19:26
$begingroup$
-1 to 1 is the interval. can you add it too?
$endgroup$
– Allic Mendonca
Jan 31 at 19:27