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A complex matrix U is special unitary if it is unitary and its matrix determinant equals 1. For real numbers, the analogue of a unitary matrix is an orthogonal matrix.
SU (3) group. The special unitary group SU is the group of unitary matrices whose determinant is equal to 1. [1] This set is closed under matrix multiplication. All transformations characterized by the special unitary group leave norms unchanged. The SU (3) symmetry appears in the light quark flavour symmetry (among up, down, and strange quarks ...
These matrices are traceless, Hermitian, and obey the extra trace orthonormality relation, so they can generate unitary matrix group elements of SU (3) through exponentiation. [1] These properties were chosen by Gell-Mann because they then naturally generalize the Pauli matrices for SU (2) to SU (3), which formed the basis for Gell-Mann's quark model. [2] Gell-Mann's generalization further ...
Schur decomposition. In the mathematical discipline of linear algebra, the Schur decomposition or Schur triangulation, named after Issai Schur, is a matrix decomposition. It allows one to write an arbitrary complex square matrix as unitarily similar to an upper triangular matrix whose diagonal elements are the eigenvalues of the original matrix.
In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix. rotates points in the xy plane counterclockwise through an angle θ about the origin of a two-dimensional Cartesian coordinate system.
The Schur complement arises naturally in solving a system of linear equations such as [7] . Assuming that the submatrix is invertible, we can eliminate from the equations, as follows. Substituting this expression into the second equation yields. We refer to this as the reduced equation obtained by eliminating from the original equation.
Matrix decomposition. In the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions; each finds use among a particular class of problems.
Invariants of tensors. In mathematics, in the fields of multilinear algebra and representation theory, the principal invariants of the second rank tensor are the coefficients of the characteristic polynomial [1] , where is the identity operator and are the roots of the polynomial and the eigenvalues of . More broadly,any scalar-valued function ...