List of matrices

Listed below are some important classes of matrices used in mathematics:

• Diagonal matrix - All entries not on the main diagonal (the diagonal from the upper left to the lower right corner) are zero. Especially easy to raise to a power.
• Diagonalizable matrix - A matrix similar to a diagonal matrix. It has a complete set of linearly independent eigenvectors.
• Normal matrix - It has a complete set of orthonormal eigenvectors.

• Symmetric matrix - A matrix that is its own transpose.
• Anti-symmetric matrix
• Hilbert matrix - A matrix with elements H_ij = (i + j - 1)^-1
• Hermitian matrix - A matrix that is its own conjugate transpose. It is a normal matrix.
• Positive definite matrix - Hermitian matrix with every eigenvalue positive.

• Orthogonal matrix - A matrix which has the same inverse and transpose, can represent a rotation.
• Unitary matrix - A matrix whose conjugate transpose is its inverse.

• Positive matrix - A matrix with all numbers > 0.
• Nonnegative matrix - A matrix with all numbers ≥ 0.
• Totally positive matrix - Determinants of all its square submatrices are positive. It is used in generating the reference points of Bézier curve in computer graphics.
• Stochastic matrix - A positive matrix describing a stochastic process. The sum of entries of any row is one.
• Permutation matrix - Matrix representation of a permutation.
• Hankel matrix
• Toeplitz matrix
• Vandermonde matrix
• Cartan matrix
• Coxeter matrix
• Invertible matrix
• Symplectic matrix
• Triangular matrix