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

• $\mathrm{GL}(n)$: invertible matrices

• $\mathrm{SU}(n)$: unitary matrices with determinant $1$

• $\mathrm{O}(n)$: orthogonal matrices

• $\mathrm{SO}(n)$: orthogonal matrices with determinant $1$ (http://planetmath.org/RotationMatrix)

• normal matrices

• positive definite matrices

• symmetric matrices, antisymmetric matrices, Hermitian matrices, anti-Hermitian matrices

• $\mathrm{Sp}(2n)$: symplectic matrices (also called $\mathrm{Sp}(n)$)

Special matrices

• zero matrix

• identity matrix

• Hilbert matrix

• Vandermonde matrix

• Toeplitz matrix

• Pascal matrix

• Cauchy matrix

• M-matrix

• magic square

• Latin square

Title	matrices of special form
Canonical name	MatricesOfSpecialForm
Date of creation	2013-03-22 14:13:49
Last modified on	2013-03-22 14:13:49
Owner	matte (1858)
Last modified by	matte (1858)
Numerical id	15
Author	matte (1858)
Entry type	Definition
Classification	msc 15-00