How to find an orthogonal basis?
Understand the Problem
The question is asking about the process or methods used to find an orthogonal basis in a vector space. This involves understanding concepts from linear algebra, specifically techniques like the Gram-Schmidt process.
Answer
Use the Gram-Schmidt process.
The final answer is to use the Gram-Schmidt process to convert a given basis into an orthogonal basis.
Answer for screen readers
The final answer is to use the Gram-Schmidt process to convert a given basis into an orthogonal basis.
More Information
The Gram-Schmidt process not only helps in finding an orthogonal basis but also an orthonormal basis if you normalize the vectors.
Tips
A common mistake is not correctly subtracting the projections, which can result in vectors that are not orthogonal.
Sources
- 6.4 Finding orthogonal bases - Understanding Linear Algebra - understandinglinearalgebra.org
- Finding Orthogonal Bases - Mathematics LibreTexts - math.libretexts.org
- Gram-Schmidt Method – Calculus Tutorials - math.hmc.edu
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