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	sine of angle of triangle SinesLaw sines law SinesLawProof sines law proof sines law proof SinesLawProof1 Singleton singleton SinglyEvenNumber singly even number SingmastersConjecture Singmaster’s conjecture Singular singular SingularFunction singular function SingularMeasure singular measure SingularSet singular set SingularSolution singular solution SingularValueDecomposition singular value decomposition