What does orthogonalize mean?
Orthogonalize is a technical verb meaning to make a set of vectors, functions, or other mathematical objects mutually perpendicular or otherwise orthogonal. In linear algebra, the process is used to put a basis or collection of directions into a form in which each member is independent of the others. It also appears in numerical analysis, signal processing, statistics, and machine learning, where orthogonalized coordinates, residuals, features, or columns can simplify calculations and reduce unwanted correlation. The word is most often transitive: a researcher may orthogonalize the vectors or orthogonalize the data before fitting a model. Orthogonalization can be achieved through transformations such as Gram–Schmidt, but the verb does not imply a particular method. Outside technical writing, it may evoke making directions deliberately perpendicular, though that figurative use is uncommon. It is a precise and useful term because it names both the condition of orthogonality and the action of bringing it about.
verbTo transform a set of vectors, functions, or other mathematical objects so that they are mutually orthogonal, or perpendicular in the relevant mathematical sense. It may also refer more generally to making directions or features independent of one another.
- To transform mathematical objects so that they are mutually orthogonal or perpendicular.
"The algorithm uses Gram–Schmidt orthogonalization to orthogonalize the vectors before solving the system."
"We orthogonalize the basis to ensure that each vector is perpendicular to the others."
"The preprocessing step orthogonalizes the features before the model is trained."
Orthogonalize gives tangled directions a clean, right-angled reset.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does orthogonalize come from?
Orthogonalize was formed in English from the established adjective orthogonal by adding the productive suffix -ize, turning a property into an action. Orthogonal comes through Latin from Greek orthos, meaning “straight,” “upright,” or “correct,” and gōnia, meaning “angle,” reflecting its geometrical association with right angles. Related English forms include orthogonal, orthogonality, orthogonally, and orthogon.
Related word forms
How orthogonalize is actually used
This is primarily a technical verb used in linear algebra, numerical analysis, signal processing, statistics, and machine learning. It is usually transitive and is most naturally followed by an object such as vectors, a basis, coordinates, residuals, columns, or features. The British spelling is usually “orthogonalise.”