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- Pascal_matrix abstract "In mathematics, particularly matrix theory and combinatorics, the Pascal matrix is an infinite matrix containing the binomial coefficients as its elements. There are three ways to achieve this: as either an upper-triangular matrix, a lower-triangular matrix, or a symmetric matrix. The 5×5 truncations of these are shown below.Upper triangular: lower triangular: symmetric: These matrices have the pleasing relationship Sn = LnUn. From this it is easily seen that all three matrices have determinant 1, as the determinant of a triangular matrix is simply the product of its diagonal elements, which are all 1 for both Ln and Un. In other words, matrices Sn, Ln, and Un are unimodular, with Ln and Un having trace n.The elements of the symmetric Pascal matrix are the binomial coefficients, i.e. In other words,Thus the trace of Sn is given bywith the first few terms given by the sequence 1, 3, 9, 29, 99, 351, 1275, … (sequence A006134 in OEIS).".
- Pascal_matrix wikiPageExternalLink 04_1_gaussmatrix.pdf.
- Pascal_matrix wikiPageExternalLink index.htm.
- Pascal_matrix wikiPageExternalLink 01_1_binomialmatrix.pdf.
- Pascal_matrix wikiPageExternalLink Edelman189-197.pdf.
- Pascal_matrix wikiPageExternalLink Erf.html.
- Pascal_matrix wikiPageExternalLink GaussianFunction.html.
- Pascal_matrix wikiPageExternalLink HermitePolynomial.html.
- Pascal_matrix wikiPageExternalLink digbib.cgi?PPN266833020_0065.
- Pascal_matrix wikiPageID "7833211".
- Pascal_matrix wikiPageRevisionID "592750287".
- Pascal_matrix hasPhotoCollection Pascal_matrix.
- Pascal_matrix subject Category:Matrices.
- Pascal_matrix subject Category:Triangles_of_numbers.
- Pascal_matrix type Abstraction100002137.
- Pascal_matrix type Arrangement107938773.
- Pascal_matrix type Array107939382.
- Pascal_matrix type Attribute100024264.
- Pascal_matrix type Figure113862780.
- Pascal_matrix type Group100031264.
- Pascal_matrix type Matrices.
- Pascal_matrix type Matrix108267640.
- Pascal_matrix type PlaneFigure113863186.
- Pascal_matrix type Polygon113866144.
- Pascal_matrix type Shape100027807.
- Pascal_matrix type Triangle113879320.
- Pascal_matrix type TrianglesOfNumbers.
- Pascal_matrix comment "In mathematics, particularly matrix theory and combinatorics, the Pascal matrix is an infinite matrix containing the binomial coefficients as its elements. There are three ways to achieve this: as either an upper-triangular matrix, a lower-triangular matrix, or a symmetric matrix. The 5×5 truncations of these are shown below.Upper triangular: lower triangular: symmetric: These matrices have the pleasing relationship Sn = LnUn.".
- Pascal_matrix label "Pascal matrix".
- Pascal_matrix label "Матрица Паскаля".
- Pascal_matrix sameAs Matrice_de_Pascal.
- Pascal_matrix sameAs m.026fnd9.
- Pascal_matrix sameAs Q7141739.
- Pascal_matrix sameAs Q7141739.
- Pascal_matrix sameAs Pascal_matrix.
- Pascal_matrix wasDerivedFrom Pascal_matrix?oldid=592750287.
- Pascal_matrix isPrimaryTopicOf Pascal_matrix.