inner product orthogonal complement [on hold]

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Consider the vector space $mathbb R_2[x]$ with the inner product $langle cdot,cdotrangle$ given by $$langle p, qrangle = p(-1)q(-1) + p(0)q(0) + p(1)q(1).$$ (You need not prove that $langlecdot,cdotrangle$ is an inner product.)



Let $U$ be the subspace of $mathbb R_2[x]$ consisting of all polynomials of degree at most $1$, i.e. $U = mathbb R_1[x]$.



  1. Find the orthogonal complement of $U$.

  2. Find the polynomial in $U$ which is closest to $-3x^2 + x$.




inner-product-space




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put on hold as off-topic by José Carlos Santos, Jendrik Stelzner, Shailesh, Brahadeesh, Key Flex 18 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, Jendrik Stelzner, Shailesh, Brahadeesh, Key Flex
If this question can be reworded to fit the rules in the help center, please edit the question.












  • Hint: what is the definition of the orthogonal complement of $X$, $X^perp$?
    – Sean Roberson
    yesterday














up vote
-2
down vote

favorite












I have no idea how to solve this question.




Consider the vector space $mathbb R_2[x]$ with the inner product $langle cdot,cdotrangle$ given by $$langle p, qrangle = p(-1)q(-1) + p(0)q(0) + p(1)q(1).$$ (You need not prove that $langlecdot,cdotrangle$ is an inner product.)



Let $U$ be the subspace of $mathbb R_2[x]$ consisting of all polynomials of degree at most $1$, i.e. $U = mathbb R_1[x]$.



  1. Find the orthogonal complement of $U$.

  2. Find the polynomial in $U$ which is closest to $-3x^2 + x$.




inner-product-space




share|cite|improve this question













put on hold as off-topic by José Carlos Santos, Jendrik Stelzner, Shailesh, Brahadeesh, Key Flex 18 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, Jendrik Stelzner, Shailesh, Brahadeesh, Key Flex
If this question can be reworded to fit the rules in the help center, please edit the question.












  • Hint: what is the definition of the orthogonal complement of $X$, $X^perp$?
    – Sean Roberson
    yesterday












up vote
-2
down vote

favorite









up vote
-2
down vote

favorite











I have no idea how to solve this question.




Consider the vector space $mathbb R_2[x]$ with the inner product $langle cdot,cdotrangle$ given by $$langle p, qrangle = p(-1)q(-1) + p(0)q(0) + p(1)q(1).$$ (You need not prove that $langlecdot,cdotrangle$ is an inner product.)



Let $U$ be the subspace of $mathbb R_2[x]$ consisting of all polynomials of degree at most $1$, i.e. $U = mathbb R_1[x]$.



  1. Find the orthogonal complement of $U$.

  2. Find the polynomial in $U$ which is closest to $-3x^2 + x$.




inner-product-space




share|cite|improve this question













I have no idea how to solve this question.




Consider the vector space $mathbb R_2[x]$ with the inner product $langle cdot,cdotrangle$ given by $$langle p, qrangle = p(-1)q(-1) + p(0)q(0) + p(1)q(1).$$ (You need not prove that $langlecdot,cdotrangle$ is an inner product.)



Let $U$ be the subspace of $mathbb R_2[x]$ consisting of all polynomials of degree at most $1$, i.e. $U = mathbb R_1[x]$.



  1. Find the orthogonal complement of $U$.

  2. Find the polynomial in $U$ which is closest to $-3x^2 + x$.





inner-product-space





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited yesterday









an4s

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Benny.Y

1




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put on hold as off-topic by José Carlos Santos, Jendrik Stelzner, Shailesh, Brahadeesh, Key Flex 18 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, Jendrik Stelzner, Shailesh, Brahadeesh, Key Flex
If this question can be reworded to fit the rules in the help center, please edit the question.




put on hold as off-topic by José Carlos Santos, Jendrik Stelzner, Shailesh, Brahadeesh, Key Flex 18 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, Jendrik Stelzner, Shailesh, Brahadeesh, Key Flex
If this question can be reworded to fit the rules in the help center, please edit the question.











  • Hint: what is the definition of the orthogonal complement of $X$, $X^perp$?
    – Sean Roberson
    yesterday
















  • Hint: what is the definition of the orthogonal complement of $X$, $X^perp$?
    – Sean Roberson
    yesterday















Hint: what is the definition of the orthogonal complement of $X$, $X^perp$?
– Sean Roberson
yesterday




Hint: what is the definition of the orthogonal complement of $X$, $X^perp$?
– Sean Roberson
yesterday















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