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 $1$
• 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