In linear algebra, an invertible complex square matrix U is unitary if its matrix inverse U−1 equals its conjugate transpose U*, that is, if U ∗ U = U...

theorem applies: Proposition—A matrix A is normal if and only if there exist a diagonal matrix Λ and a unitary matrix U such that A = UΛU*. The diagonal...

the unitary group of degree n, denoted U(n), is the group of n × n unitary matrices, with the group operation of matrix multiplication. The unitary group...

symmetric matrix can be 'diagonalized' using a unitary matrix: thus if A {\displaystyle A} is a complex symmetric matrix, there is a unitary matrix U {\displaystyle...

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...

to: m-by-n matrix A with linearly independent columns Decomposition: A = Q R {\displaystyle A=QR} where Q {\displaystyle Q} is a unitary matrix of size m-by-m...

m\times m} ⁠ complex unitary matrix, Σ {\displaystyle \mathbf {\Sigma } } is an m × n {\displaystyle m\times n} rectangular diagonal matrix with non-negative...

where Q−1 is the inverse of Q. An orthogonal matrix Q is necessarily invertible (with inverse Q−1 = QT), unitary (Q−1 = Q∗), where Q∗ is the Hermitian adjoint...

physics, the Cabibbo–Kobayashi–Maskawa matrix, CKM matrix, quark mixing matrix, or KM matrix is a unitary matrix that contains information on the strength...

theory (QFT). More formally, in the context of QFT, the S-matrix is defined as the unitary matrix connecting sets of asymptotically free particle states...

only if it is simultaneously diagonalizable by a unitary matrix; that is, there exists a unitary matrix U {\displaystyle U} such that U ∗ A U {\displaystyle...

determinant +1. The complex analogue of an orthogonal matrix is a unitary matrix. A real or complex square matrix A {\displaystyle A} is called normal if A ∗ A...

notion of a unitary operator is a generalization of the notion of a unitary matrix. Orthogonal matrices are the special case of unitary matrices in which...

a matrix decomposition of a matrix A {\displaystyle A} into a unitary matrix P {\displaystyle P} and a Hessenberg matrix H {\displaystyle H} such that...

2^{n}\times 2^{n}} unitary matrix, and the set of all such gates with the group operation of matrix multiplication is the unitary group U(2n). The quantum...

transformations are unitary matrices, and since the multiplication of unitary matrices is itself a unitary matrix, this gives us the unitary matrix of the QR decomposition)...

real symmetric matrix and more generally a Hermitian matrix, and a unitary matrix, is never defective; more generally, a normal matrix (which includes...

diagonalizing a normal matrix A {\displaystyle \mathbf {A} } by finding its eigenvalues and eigenvectors, forming the unitary matrix U {\displaystyle \mathbf...

real rotation matrix is the identity matrix. Likewise, the Gram matrix of the rows or columns of a unitary matrix is the identity matrix. The rank of the...

In mathematics, a triangular matrix is a special kind of square matrix. A square matrix is called lower triangular if all the entries above the main diagonal...

transformation is thus an arbitrary unitary change of basis on the space of all state vectors. U is an arbitrary unitary matrix, a complex rotation in phase...

complex matrix A {\displaystyle A} is a factorization of the form A = U P {\displaystyle A=UP} , where U {\displaystyle U} is a unitary matrix, and P {\displaystyle...

^{-1}.} A square complex matrix whose transpose is equal to its conjugate inverse is called a unitary matrix; that is, A is unitary if A T = A − 1 ¯ . {\displaystyle...

{H}}\right)} Bivector (complex) Hermitian matrix Normal matrix Skew-symmetric matrix Unitary matrix Horn & Johnson (1985), §4.1.1; Meyer (2000), §3...

Householder matrix is built through the identity matrix) Square root of a 2 by 2 identity matrix Unitary matrix Zero matrix "Identity matrix: intro to identity...

The Wigner D-matrix is a unitary matrix in an irreducible representation of the groups SU(2) and SO(3). It was introduced in 1927 by Eugene Wigner, and...

such norms are referred to as matrix norms. Matrix norms differ from vector norms in that they must also interact with matrix multiplication. Given a field...

any real skew-symmetric matrix can be diagonalized by a unitary matrix. Since the eigenvalues of a real skew-symmetric matrix are imaginary, it is not...

{\displaystyle k\times n} matrix B {\displaystyle B} and if Q {\displaystyle Q} is any unitary k × k {\displaystyle k\times k} matrix (meaning Q ∗ Q = Q Q...

Look up unitary in Wiktionary, the free dictionary. Unitary may refer to: Unitary divisor Unitary element Unitary group Unitary matrix Unitary morphism...