the inverse of a square matrix does not exist when singular or degenerate.
when does the inverse of a square matrix not exist?
singular or degenerate
a square matrix that is not invertible is called singular or degenerate. a square matrix is singular if and only if its determinant is 0. singular matrices are rare in the sense that a square matrix randomly selected from a continuous uniform distribution on its entries will almost never be singular.
invertible matrix
bullet::::- hessenberg matrix, a square matrix that has either zero entries below the first subdiagonal, zero entries above the first superdiagonal, or both





























bullet::::- hessian matrix, a square matrix of second-order partial derivatives of a scalar-valued function, or scalar field, that describes the local curvature of a function of many variables





























bullet::::- hierarchical matrix, a data-sparse approximation of a non-sparse matrix





























bullet::::- hilbert matrix, a square matrix with entries being the unit fractions





























bullet::::- hollow matrix, a square matrix or related classes of matrix





























bullet::::- hurwitz matrix, a square matrix constructed with coefficients of a real polynomial
h-matrix