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- Moore_matrix abstract "In linear algebra, a Moore matrix, introduced by E. H. Moore (1896), is a matrix defined over a finite field. When it is a square matrix its determinant is called a Moore determinant (this is unrelated to the Moore determinant of a quaternionic Hermitian matrix). The Moore matrix has successive powers of the Frobenius automorphism applied to the first column, so it is an m × n matrixorfor all indices i and j. (Some authors use the transpose of the above matrix.)The Moore determinant of a square Moore matrix (so m = n) can be expressed as:where c runs over a complete set of direction vectors, made specific by having the last non-zero entry equal to 1, i.e.In particular the Moore determinant vanishes if and only if the elements in the left hand column are linearly dependent over the finite field of order q. So it is analogous to the Wronskian of several functions.Dickson used the Moore determinant in finding the modular invariants of the general linear group over a finite field.".
- Moore_matrix wikiPageExternalLink lineargroupswith00dickuoft.
- Moore_matrix wikiPageID "18464794".
- Moore_matrix wikiPageRevisionID "581835886".
- Moore_matrix authorlink "E. H. Moore".
- Moore_matrix first "E. H.".
- Moore_matrix hasPhotoCollection Moore_matrix.
- Moore_matrix last "Moore".
- Moore_matrix year "1896".
- Moore_matrix subject Category:Determinants.
- Moore_matrix subject Category:Matrices.
- Moore_matrix type Abstraction100002137.
- Moore_matrix type Arrangement107938773.
- Moore_matrix type Array107939382.
- Moore_matrix type Cognition100023271.
- Moore_matrix type CognitiveFactor105686481.
- Moore_matrix type Determinant105692419.
- Moore_matrix type Determinants.
- Moore_matrix type Group100031264.
- Moore_matrix type Matrices.
- Moore_matrix type Matrix108267640.
- Moore_matrix type PsychologicalFeature100023100.
- Moore_matrix comment "In linear algebra, a Moore matrix, introduced by E. H. Moore (1896), is a matrix defined over a finite field. When it is a square matrix its determinant is called a Moore determinant (this is unrelated to the Moore determinant of a quaternionic Hermitian matrix). The Moore matrix has successive powers of the Frobenius automorphism applied to the first column, so it is an m × n matrixorfor all indices i and j.".
- Moore_matrix label "Matriz de Moore".
- Moore_matrix label "Moore matrix".
- Moore_matrix sameAs Matriz_de_Moore.
- Moore_matrix sameAs m.04d_slx.
- Moore_matrix sameAs Q6908274.
- Moore_matrix sameAs Q6908274.
- Moore_matrix sameAs Moore_matrix.
- Moore_matrix wasDerivedFrom Moore_matrix?oldid=581835886.
- Moore_matrix isPrimaryTopicOf Moore_matrix.