matrices of special form

The aim of the present entry is to list matrices with special properties.

Restriction on form

•
diagonal matrices
•
anti-diagonal matrices
•
triangular matrices
•
block matrices of either form above or of some other form
•
nilpotent matrices
•
elementary matrices
•
Hadamard matrices
•
partly decomposable matrices
•
fully indecomposable matrices
•
nearly decomposable matrices
•
doubly stochastic matrices
•
stochastic matrices

In numerical applications, sparse matrices (matrices with few nonzero entries) are important; these can be of any of the forms above.

Other restrictions

•
singular matrices
•
$\\operatorname{GL}(n)$ : invertible matrices
•
$\\operatorname{SU}(n)$ : unitary matrices with determinant $1$
•
$\\operatorname{O}(n)$ : orthogonal matrices
•
$\\operatorname{SO}(n)$ :orthogonal matrices with determinant $1$ (http://planetmath.org/RotationMatrix)
•
normal matrices
•
positive definite matrices
•
symmetric matrices, antisymmetric matrices, Hermitian matrices, anti-Hermitian matrices
•
$\\operatorname{Sp}(2n)$ : symplectic matrices (also called $\\operatorname{Sp}(n)$ )

Special matrices

•
zero matrix
•
identity matrix
•
Hilbert matrix
•
Vandermonde matrix
•
Toeplitz matrix
•
Pascal matrix
•
Cauchy matrix
•
M-matrix
•
magic square
•
Latin square

单词	MatricesOfSpecialForm
释义	matrices of special form The aim of the present entry is to list matrices with special properties. Restriction on form • diagonal matrices • anti-diagonal matrices • triangular matrices • block matrices of either form above or of some other form • nilpotent matrices • elementary matrices • Hadamard matrices • partly decomposable matrices • fully indecomposable matrices • nearly decomposable matrices • doubly stochastic matrices • stochastic matrices In numerical applications, sparse matrices (matrices with few nonzero entries) are important; these can be of any of the forms above. Other restrictions • singular matrices • $\\operatorname{GL}(n)$ : invertible matrices • $\\operatorname{SU}(n)$ : unitary matrices with determinant $1$ • $\\operatorname{O}(n)$ : orthogonal matrices • $\\operatorname{SO}(n)$ :orthogonal matrices with determinant $1$ (http://planetmath.org/RotationMatrix) • normal matrices • positive definite matrices • symmetric matrices, antisymmetric matrices, Hermitian matrices, anti-Hermitian matrices • $\\operatorname{Sp}(2n)$ : symplectic matrices (also called $\\operatorname{Sp}(n)$ ) Special matrices • zero matrix • identity matrix • Hilbert matrix • Vandermonde matrix • Toeplitz matrix • Pascal matrix • Cauchy matrix • M-matrix • magic square • Latin square
随便看	range voting RankLieAlgebra rank (Lie algebra) RanknullityTheorem rank-nullity theorem rank-nullity theorem RanknullityTheorem1 RankOfALinearMapping rank of a linear mapping RankOfAMatrix rank of a matrix RankOfAnEllipticCurve rank of an elliptic curve RankselectedPoset rank-selected poset RareNumbers Rare numbers RateOfReturn rate of return RationalAlgebraicIntegers rational algebraic integers RationalAndIrrational rational and irrational RationalBriggsianLogarithmsOfIntegers rational Briggsian logarithms of integers