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- Sylvester's_determinant_theorem abstract "In matrix theory, Sylvester's determinant theorem is a theorem useful for evaluating certain types of determinants. It is named after James Joseph Sylvester, who stated this theorem without proof.The theorem states that if A, B are matrices of size p × n and n × p respectively, thenwhere Ia is the identity matrix of order a.This can be seen for invertible A, B by conjugating I + AB by A-1, then extended to arbitrary square matrices by density of invertible matrices, and then to arbitraryrectangular matrices by adding zero column or row vectors as necessary.It is closely related to the Matrix determinant lemma and its generalization. It is the determinant analogue of the Woodbury matrix identity for matrix inverses.".
- Sylvester's_determinant_theorem wikiPageID "8641870".
- Sylvester's_determinant_theorem wikiPageRevisionID "596861375".
- Sylvester's_determinant_theorem hasPhotoCollection Sylvester's_determinant_theorem.
- Sylvester's_determinant_theorem subject Category:Determinants.
- Sylvester's_determinant_theorem subject Category:Linear_algebra.
- Sylvester's_determinant_theorem subject Category:Matrix_theory.
- Sylvester's_determinant_theorem subject Category:Theorems_in_algebra.
- Sylvester's_determinant_theorem type Abstraction100002137.
- Sylvester's_determinant_theorem type Cognition100023271.
- Sylvester's_determinant_theorem type CognitiveFactor105686481.
- Sylvester's_determinant_theorem type Communication100033020.
- Sylvester's_determinant_theorem type Determinant105692419.
- Sylvester's_determinant_theorem type Determinants.
- Sylvester's_determinant_theorem type Message106598915.
- Sylvester's_determinant_theorem type Proposition106750804.
- Sylvester's_determinant_theorem type PsychologicalFeature100023100.
- Sylvester's_determinant_theorem type Statement106722453.
- Sylvester's_determinant_theorem type Theorem106752293.
- Sylvester's_determinant_theorem type TheoremsInAlgebra.
- Sylvester's_determinant_theorem comment "In matrix theory, Sylvester's determinant theorem is a theorem useful for evaluating certain types of determinants.".
- Sylvester's_determinant_theorem label "Sylvester's determinant theorem".
- Sylvester's_determinant_theorem sameAs m.027c5vy.
- Sylvester's_determinant_theorem sameAs Q7660749.
- Sylvester's_determinant_theorem sameAs Q7660749.
- Sylvester's_determinant_theorem sameAs Sylvester's_determinant_theorem.
- Sylvester's_determinant_theorem wasDerivedFrom Sylvester's_determinant_theorem?oldid=596861375.
- Sylvester's_determinant_theorem isPrimaryTopicOf Sylvester's_determinant_theorem.