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skew-Hermitian or anti-Hermitian if its conjugate transpose is the negative of the original matrix. That is, the matrix A {\displaystyle A} is skew-Hermitian...

form singular values. Among complex matrices, all unitary, Hermitian, and skew-Hermitian matrices are normal, with all eigenvalues being unit modulus...

for all v in V; skew-symmetric or antisymmetric if B(v, w) = −B(w, v) for all v, w in V; Proposition Every alternating form is skew-symmetric. Proof...

special automorphism groups of symmetric or skew-symmetric bilinear forms and Hermitian or skew-Hermitian sesquilinear forms defined on real, complex...

symmetric forms, skew-symmetric forms (= symplectic forms), Hermitian forms, and skew-Hermitian forms. More briefly, one may refer to quadratic, skew-quadratic...

Lie group of dimension n2. The Lie algebra of U(n) consists of n × n skew-Hermitian matrices, with the Lie bracket given by the commutator. The general...

matrix ensembles are random Hermitian matrices with density on the space of real symmetric/Hermitian/quaternionic Hermitian matrices, which is of the form...

matrix — a matrix describing the statistical state of a quantum system. Hermitian, non-negative and with trace 1. Fundamental matrix (computer vision) —...

characteristic not 2, alternation is equivalent to skew-symmetry. If the characteristic is 2, the skew-symmetry is implied by, but does not imply alternation...

mathematics, a Hermitian symmetric space is a Hermitian manifold which at every point has an inversion symmetry preserving the Hermitian structure. First...

symmetric, and if X is skew-symmetric then eX is orthogonal. If X is Hermitian then eX is also Hermitian, and if X is skew-Hermitian then eX is unitary....

Lie algebra g that is closed under the commutators and consists of skew-hermitian matrices. It follows that u0 is a real Lie subalgebra of g, that its...

Riemannian metric for complex manifolds, called a Hermitian metric. Like a Riemannian metric, a Hermitian metric consists of a smoothly varying, positive...

CPn endowed with a Hermitian form. This metric was originally described in 1904 and 1905 by Guido Fubini and Eduard Study. A Hermitian form in (the vector...

but with contraction using the hermitian form, this construction gives a spinor space at every point of an almost Hermitian manifold and is the reason why...

{\displaystyle \mathbb {C} } . (Indeed, i times a skew-hermitian matrix is hermitian, rather than skew-hermitian.) Likewise, the unitary group U ( n ) {\displaystyle...

hermitian conjugation. These two views are essentially equivalent, as the real algebra can be constructed from the complex algebra by taking the skew-Hermitian...

{\displaystyle A} is Hermitian, then every eigenvalue is real. The same is true of any symmetric real matrix. If A {\displaystyle A} is not only Hermitian but also...

matrices are real symmetric (or skew-symmetric) matrices (e.g. covariance matrices) and Hermitian matrices (or skew-Hermitian matrices). See spectral theorems...

is denoted by T r {\displaystyle {\rm {Tr}}} . A density matrix is a Hermitian, positive semi-definite matrix of trace one. It allows for the description...