the Gram-Schmidt process does: orthogonalizes a set of vectors

Gram-Schmidt orthogonalizes vectors in Rⁿ

The Gram-Schmidt process transforms a set of linearly independent vectors into an orthogonal set. This is crucial for simplifying problems in linear algebra and numerical analysis.

Example

Given vectors v1, v2 in R², applying Gram-Schmidt yields u1 and u2, which are orthogonal to each other.

Remember this

Orthogonal vectors simplify computations and are foundational in many applications, such as solving linear systems and performing projections.

Text adapted from Wikipedia, licensed under CC BY-SA 4.0.

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