How to find the orthogonal basis?

Thread starter amninder15
Start date Apr 14, 2012
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Basis Orthogonal

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SUMMARY

The discussion focuses on the process of finding an orthogonal basis in linear algebra, specifically emphasizing the importance of inner products. Participants clarify that there is not a unique orthogonal basis that extends a given vector, denoted as u1. The key takeaway is the necessity of understanding inner products to approach the problem effectively.

PREREQUISITES

Linear algebra concepts, particularly orthogonal vectors
Understanding of inner product spaces
Familiarity with basis extension in vector spaces
Knowledge of Gram-Schmidt process for orthogonalization

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Study the Gram-Schmidt process for constructing orthogonal bases
Explore inner product definitions and properties in vector spaces
Learn about orthogonal complements and their significance
Investigate applications of orthogonal bases in computational methods

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Students and professionals in mathematics, particularly those studying linear algebra, as well as educators seeking to deepen their understanding of orthogonal bases and inner product spaces.

Apr 14, 2012

amninder15

Can somebody help me how to approach this problem.I am having trouble finding the orthogonal basis.

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Apr 14, 2012

micromass

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You don't need to explicitely find a orthogonal basis (note that I said "a" and not "the": there is not a unique basis that extends u₁). You just need to find s.

Think of inner products.

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