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11 relations: Comparison matrix, Gauss–Seidel method, Hurwitz matrix, Invertible matrix, Iterative method, L-matrix, M-matrix, Matrix (mathematics), P-matrix, Perron–Frobenius theorem, Z-matrix (mathematics).
Comparison matrix
In linear algebra, let be a complex matrix.
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Gauss–Seidel method
In numerical linear algebra, the Gauss–Seidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a linear system of equations.
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Hurwitz matrix
In mathematics, a Hurwitz matrix, or Routh–Hurwitz matrix, in engineering stability matrix, is a structured real square matrix constructed with coefficients of a real polynomial.
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Invertible matrix
In linear algebra, an n-by-n square matrix A is called invertible (also nonsingular or nondegenerate) if there exists an n-by-n square matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication.
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Iterative method
In computational mathematics, an iterative method is a mathematical procedure that uses an initial guess to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones.
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L-matrix
In mathematics, the class of L-matrices are those matrices whose off-diagonal entries are less than or equal to zero and whose diagonal entries are positive; that is, an L-matrix L satisfies.
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M-matrix
In mathematics, especially linear algebra, an M-matrix is a ''Z''-matrix with eigenvalues whose real parts are nonnegative.
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Matrix (mathematics)
In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
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P-matrix
In mathematics, a P-matrix is a complex square matrix with every principal minor > 0.
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Perron–Frobenius theorem
In linear algebra, the Perron–Frobenius theorem, proved by and, asserts that a real square matrix with positive entries has a unique largest real eigenvalue and that the corresponding eigenvector can be chosen to have strictly positive components, and also asserts a similar statement for certain classes of nonnegative matrices.
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Z-matrix (mathematics)
In mathematics, the class of Z-matrices are those matrices whose off-diagonal entries are less than or equal to zero; that is, a Z-matrix Z satisfies Note that this definition coincides precisely with that of a negated Metzler matrix or quasipositive matrix, thus the term quasinegative matrix appears from time to time in the literature, though this is rare and usually only in contexts where references to quasipositive matrices are made.
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References
[1] https://en.wikipedia.org/wiki/H-matrix_(iterative_method)
