Are orthogonal vectors linearly independent?
Understand the Problem
The question is asking whether orthogonal vectors are always linearly independent. It implies a need to analyze the definitions of orthogonal vectors and linear independence in a vector space.
Answer
Yes
The final answer is yes, orthogonal vectors are linearly independent.
Answer for screen readers
The final answer is yes, orthogonal vectors are linearly independent.
More Information
According to linear algebra, any orthogonal set of vectors is automatically linearly independent. This means that no vector in the set can be expressed as a linear combination of the others.
Tips
Confusing orthogonality with linear independence. While all orthogonal vectors are linearly independent, not all linearly independent vectors are orthogonal.
Sources
- Lecture 17: Orthogonality - people.math.harvard.edu
- Proving that orthogonal vectors are linearly independent - math.stackexchange.com
- Orthogonality implies Linear Independence ( Orthogonal ... - YouTube - youtube.com
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