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Z-matrix (mathematics)

Index 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. [1]

11 relations: Chemistry, Hurwitz matrix, Invertible matrix, Jacobian matrix and determinant, L-matrix, M-matrix, Mathematics, Matrix (mathematics), Metzler matrix, P-matrix, Z-matrix (chemistry).

Chemistry

Chemistry is the scientific discipline involved with compounds composed of atoms, i.e. elements, and molecules, i.e. combinations of atoms: their composition, structure, properties, behavior and the changes they undergo during a reaction with other compounds.

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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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Jacobian matrix and determinant

In vector calculus, the Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function.

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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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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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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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Metzler matrix

In mathematics, a Metzler matrix is a matrix in which all the off-diagonal components are nonnegative (equal to or greater than zero) It is named after the American economist Lloyd Metzler.

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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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Z-matrix (chemistry)

In chemistry, the Z-matrix is a way to represent a system built of atoms.

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References

[1] https://en.wikipedia.org/wiki/Z-matrix_(mathematics)

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