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

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...

} 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...

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

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

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...

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...

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...

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

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

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

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...

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

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...

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...

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

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...

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...

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

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

unitary matrix, and V ∗ {\displaystyle \mathbf {V} ^{*}} is the conjugate transpose of ⁠ V {\displaystyle \mathbf {V} } ⁠. Such decomposition always...

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

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

{\displaystyle A^{*}A} (where A ∗ {\displaystyle A^{*}} denotes the conjugate transpose of A {\displaystyle A} ). This is equivalent to assigning the largest...

{\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...

positive-semidefinite matrix P can be written as N*N, where N* denotes the conjugate transpose of N (see Decomposition of a semidefinite matrix). Then det ( P )...

defines congruence in terms of conjugate transpose (with respect to a complex inner product space) rather than transpose, but this definition has not been...

the star or asterisk denotes the conjugate transpose of the matrix, that is, the transpose of the complex conjugate of A. By the spectral theorem, real...

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