orthogonalization.

The process of transforming vectors or related components so they become mutually orthogonal under a specified inner product.

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Words that belong together

• Gram-Schmidt orthogonalization
• orthogonalization of a basis
• successive orthogonalization

On the page

Gram-Schmidt orthogonalization produced a basis with the same span as the original vectors.

The numerical method repeated the orthogonalization to reduce accumulated error.

Usage notes

Primary category: academic / formal / analytical. Lexical Type: Word. Forms: Usually uncountable; no ordinary plural in this sense. Commonness: uncommon (editorial estimate; not a corpus frequency statistic). Legacy lexical fields mirror sense 1; numbered fields keep each relevant meaning separate. Research distinction: Ohio State open linear-algebra material directly read: Gram-Schmidt orthogonalization constructs an orthogonal basis of the same subspace from an independent starting basis. Orthogonal vectors have zero inner products. Procedure, not a synonym for general statistical independence. Individually useful in research, criticism, methodology or conceptual analysis. Definitions and examples are original; no mood or intensity assigned to neutral analytical concepts. Commonness is an editorial estimate, not a frequency statistic. Writing functions: constructing an alternative basis, separating overlapping analytical directions.