In mathematics, the conjugate transpose, also known as the Hermitian transpose, of an m × n {\displaystyle m\times n} complex matrix A {\displaystyle \mathbf...

} A square complex matrix whose transpose is equal to the matrix with every entry replaced by its complex conjugate (denoted here with an overline) is...

with the notation for the conjugate transpose of a matrix, which can be thought of as a generalization of the complex conjugate. The second is preferred...

that is equal to its own conjugate transpose—that is, the element in the i-th row and j-th column is equal to the complex conjugate of the element in the...

matrices, the Hermitian adjoint is given by the conjugate transpose (also known as the Hermitian transpose). The above definition of an adjoint operator...

complex entries is said to be skew-Hermitian or anti-Hermitian if its conjugate transpose is the negative of the original matrix. That is, the matrix A {\displaystyle...

of any degree Conjugate transpose, the complex conjugate of the transpose of a matrix Harmonic conjugate in complex analysis Conjugate (graph theory)...

square matrix U is unitary if its matrix inverse U−1 equals its conjugate transpose U*, that is, if U ∗ U = U U ∗ = I , {\displaystyle U^{*}U=UU^{*}=I...

a row vector that is the conjugate transpose to a column vector v {\displaystyle v} ). In quantum mechanics, the conjugate to a ket vector  | ψ ⟩ {\displaystyle...

} For complex vectors, it is often useful to take the conjugate transpose of v , {\displaystyle \mathbf {v} ,} denoted v † {\displaystyle \mathbf...

transpose of   x   . {\displaystyle \ \mathbf {x} ~.} More generally, a Hermitian matrix (that is, a complex matrix equal to its conjugate transpose)...

symbol ' denotes the conjugate transpose. The trivial modification is simply substituting the conjugate transpose for the real transpose everywhere. The advantages...

different concept, the adjoint operator which for a matrix is the conjugate transpose. The product of a matrix with its adjugate gives a diagonal matrix...

reflector H=I-VTVH. "*larzb" applies a block reflector or its transpose/conjugate transpose as returned by "*tzrzf" to a general matrix. "*larzt" forms...

mathematics, a complex square matrix A is normal if it commutes with its conjugate transpose A*: A  normal ⟺ A ∗ A = A A ∗ . {\displaystyle A{\text{ normal}}\iff...

n}} ⁠, the transpose is denoted ⁠ A T {\displaystyle A^{\operatorname {T} }} ⁠ and the Hermitian transpose (also called conjugate transpose) is denoted...

is a Riemannian symmetric space Hermitian transpose, the transpose of a matrix and with the complex conjugate of each entry Hermitian variety, a generalisation...

In linear algebra, the transpose of a linear map between two vector spaces, defined over the same field, is an induced map between the dual spaces of...

denotes the conjugate transpose of x {\displaystyle \mathbf {x} } (conjugate of the transpose, or equivalently transpose of the conjugate). Matrix multiplication...

{\displaystyle AA^{*}=A^{*}A} , where A ∗ {\displaystyle A^{*}} is a conjugate transpose) can be eigendecomposed. For a normal matrix A (and only for a normal...

the dot product can be expressed as a matrix product involving a conjugate transpose, denoted with the superscript H: a ⋅ b = b H a . {\displaystyle \mathbf...

Hermitian matrix with complex-valued entries, which is equal to its conjugate transpose. Therefore, in linear algebra over the complex numbers, it is often...

positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g., Monte Carlo...

numbers and complex conjugation, matrices over the complex numbers and conjugate transpose, and linear operators over a Hilbert space and Hermitian adjoints...

\mathbf {U} ^{*}} denotes the conjugate transpose and U † {\displaystyle \mathbf {U} ^{\dagger }} denotes the conjugate transpose. They diagonalize using unitary...

next to a ket implies matrix multiplication. The conjugate transpose (also called Hermitian conjugate) of a bra is the corresponding ket and vice versa:...

Hermitian conjugate (also called the conjugate transpose) of A {\displaystyle A} , defined as applying both the complex conjugate and the transpose transformations...

Q−1 = QT), unitary (Q−1 = Q∗), where Q∗ is the Hermitian adjoint (conjugate transpose) of Q, and therefore normal (Q∗Q = QQ∗) over the real numbers. The...

{1}{p}}|A|^{p}+{\tfrac {1}{q}}|B|^{q},} where ∗ {\displaystyle {}^{*}} denotes the conjugate transpose of the matrix and | A | = A ∗ A . {\displaystyle |A|={\sqrt {A^{*}A}}...

G=V^{\dagger }V} , where V † {\displaystyle V^{\dagger }} is the conjugate transpose of V {\displaystyle V} . Given square-integrable functions { ℓ i...