# matrices of special form

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

## Restriction on form

• block matrices of either form above or of some other form

• fully indecomposable matrices

• nearly decomposable matrices

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

## Other restrictions

• $\operatorname{GL}(n)$: 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)

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

## Special matrices

Title matrices of special form MatricesOfSpecialForm 2013-03-22 14:13:49 2013-03-22 14:13:49 matte (1858) matte (1858) 15 matte (1858) Definition msc 15-00