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.
- 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