H-matrix can refer to various kinds of
matrices
Matrix (: matrices or matrixes) or MATRIX may refer to:
Science and mathematics
* Matrix (mathematics), a rectangular array of numbers, symbols or expressions
* Matrix (logic), part of a formula in prenex normal form
* Matrix (biology), the ...
denoted by the letter ''H'':
*
H-matrix, a matrix whose comparison matrix is an M-matrix
*
Hadamard matrix
In mathematics, an Hadamard matrix, named after the French mathematician Jacques Hadamard, is a square matrix whose entries are either +1 or −1 and whose rows are mutually orthogonal. In geometry, geometric terms, this means that each pair of r ...
, a square matrix whose entries are either +1 or −1 and whose rows are mutually orthogonal
*
Hamiltonian matrix
In mathematics, a Hamiltonian matrix is a -by- matrix such that is symmetric, where is the skew-symmetric matrix
:J =
\begin
0_n & I_n \\
-I_n & 0_n \\
\end
and is the -by- identity matrix. In other words, is Hamiltonian if and only if ...
, a 2''n'' × 2''n'' matrix ''A'' such that ''JA'' is symmetric, where ''J'' is the skew-symmetric matrix
*
Hankel matrix
In linear algebra, a Hankel matrix (or catalecticant matrix), named after Hermann Hankel, is a rectangular matrix in which each ascending skew-diagonal from left to right is constant. For example,
\qquad\begin
a & b & c & d & e \\
b & c & d & e & ...
, a square matrix in which each ascending skew-diagonal from left to right is constant
*
Hasse–Witt matrix In mathematics, the Hasse–Witt matrix ''H'' of a Algebraic curve#Singularities, non-singular algebraic curve ''C'' over a finite field ''F'' is the matrix (mathematics), matrix of the Frobenius mapping (''p''-th power mapping where ''F'' has ''q' ...
*
Hat matrix
In statistics, the projection matrix (\mathbf), sometimes also called the influence matrix or hat matrix (\mathbf), maps the vector of response values (dependent variable values) to the vector of fitted values (or predicted values). It describes ...
*
Hermitian matrix
In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the -th row and -th column is equal to the complex conjugate of the element in the ...
, a complex square matrix that is equal to its own conjugate transpose
*
Hessenberg matrix
In linear algebra, a Hessenberg matrix is a special kind of square matrix, one that is "almost" triangular. To be exact, an upper Hessenberg matrix has zero entries below the first subdiagonal, and a lower Hessenberg matrix has zero entries above ...
, a square matrix that has either zero entries below the first subdiagonal, zero entries above the first superdiagonal, or both
*
Hessian matrix
In mathematics, the Hessian matrix, Hessian or (less commonly) Hesse matrix is a square matrix of second-order partial derivatives of a scalar-valued Function (mathematics), function, or scalar field. It describes the local curvature of a functio ...
, 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
*
Hierarchical matrix
In numerical mathematics, hierarchical matrices (H-matrices)
are used as data-sparse approximations of non-sparse matrices. While a sparse matrix of dimension n can be represented efficiently in O(n) units of storage by storing only its non-zero e ...
, a data-sparse approximation of a non-sparse matrix
*
Hilbert matrix
In linear algebra, a Hilbert matrix, introduced by , is a square matrix with entries being the unit fractions
: H_ = \frac.
For example, this is the 5 × 5 Hilbert matrix:
: H = \begin
1 & \frac & \frac & \frac & \frac \\
\frac & \frac & \ ...
, a square matrix with entries being the unit fractions
*
Hollow matrix
In mathematics, a hollow matrix may refer to one of several related classes of matrix: a sparse matrix; a matrix with a large block of zeroes; or a matrix with diagonal entries all zero.
Definitions
Sparse
A ''hollow matrix'' may be one with "f ...
, a square matrix or related classes of matrix
*
Routh–Hurwitz matrix
In mathematics, the Routh–Hurwitz matrix, or more commonly just Hurwitz matrix, corresponding to a polynomial is a particular matrix whose nonzero entries are coefficients of the polynomial.
Hurwitz matrix and the Hurwitz stability criterion
N ...
, a square matrix constructed with coefficients of a real polynomial
*
Parity-check matrix
In coding theory, a parity-check matrix of a linear block code ''C'' is a matrix which describes the linear relations that the components of a codeword must satisfy. It can be used to decide whether a particular vector is a codeword and is also us ...
is often called H-matrix.
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