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.

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