The Gram-Schmidt process is a method used in linear algebra to orthogonalize a set of vectors in an inner product space, turning them into an orthonormal basis. This process involves taking a linearly independent set of vectors and transforming them into a new set that is orthogonal (perpendicular) to each other while ensuring that each vector has unit length. This concept plays a crucial role in understanding orthogonality and the structure of inner product spaces, especially when it comes to simplifying complex problems in analysis.
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