Jacobi rotation
id:
jacobi-rotation-227-2156826
title:
Jacobi rotation
text:
In numerical linear algebra, a Jacobi rotation is a rotation, Qkℓ, of a 2-dimensional linear subspace of an n-dimensional inner product space, chosen to zero a symmetric pair of off-diagonal entries of an n×n real symmetric matrix, A, when applied as a similarity transformation:
- A ↦ Q k ℓ T A Q k ℓ = A ′.
- [ ∗ ⋯ ∗ ⋱ a k k ⋯ a k ℓ ⋮ ⋮ ⋱ ⋮ ⋮ a ℓ k ⋯ a ℓ ℓ ⋱ ∗ ⋯ ∗ ] → [ ∗ ⋯ ∗ ⋱ a k k ′ ⋯ 0 ⋮ ⋮ ⋱ ⋮ ⋮ 0 ⋯ a ℓ ℓ ′ ⋱ ∗ ⋯ ∗ ]. It is the core operation in the Jacobi eigenvalue algorithm, which is
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wiki
category slug:
encyclopedia
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original url:
https://en.wikipedia.org/wiki/Jacobi_rotation
date created:
2006-07-02T12:33:21Z
date modified:
2024-09-15T07:21:39Z
main entity:
{"identifier":"Q6119655","url":"https://www.wikidata.org/entity/Q6119655"}
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13
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14