# Definitions for orthogonalizationor·thog·o·nal·iza·tion

### WiktionaryRate this definition:0.0 / 0 votes

1. orthogonalizationnoun

The process of converting a set of functions or vectors into orthogonal ones

### WikipediaRate this definition:0.0 / 0 votes

1. Orthogonalization

In linear algebra, orthogonalization is the process of finding a set of orthogonal vectors that span a particular subspace. Formally, starting with a linearly independent set of vectors {v1, ... , vk} in an inner product space (most commonly the Euclidean space Rn), orthogonalization results in a set of orthogonal vectors {u1, ... , uk} that generate the same subspace as the vectors v1, ... , vk. Every vector in the new set is orthogonal to every other vector in the new set; and the new set and the old set have the same linear span. In addition, if we want the resulting vectors to all be unit vectors, then we normalize each vector and the procedure is called orthonormalization. Orthogonalization is also possible with respect to any symmetric bilinear form (not necessarily an inner product, not necessarily over real numbers), but standard algorithms may encounter division by zero in this more general setting.

### WikidataRate this definition:0.0 / 0 votes

1. Orthogonalization

In linear algebra, orthogonalization is the process of finding a set of orthogonal vectors that span a particular subspace. Formally, starting with a linearly independent set of vectors {v1, ..., vk} in an inner product space, orthogonalization results in a set of orthogonal vectors {u1, ..., uk} that generate the same subspace as the vectors v1, ..., vk. Every vector in the new set is orthogonal to every other vector in the new set; and the new set and the old set have the same linear span. In addition, if we want the resulting vectors to all be unit vectors, then the procedure is called orthonormalization. Orthogonalization is also possible with respect to any symmetric bilinear form, but standard algorithms may encounter division by zero in this more general setting.

### Numerology

1. Chaldean Numerology

The numerical value of orthogonalization in Chaldean Numerology is: 7

2. Pythagorean Numerology

The numerical value of orthogonalization in Pythagorean Numerology is: 3

### Popularity rank by frequency of use

orthogonalization#100000#264043#333333

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"orthogonalization." Definitions.net. STANDS4 LLC, 2024. Web. 21 Apr. 2024. <https://www.definitions.net/definition/orthogonalization>.

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