Conjugate transpose information

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...

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...

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

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...

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...

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

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

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...

{\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...

}} is the transpose of z {\displaystyle z} . More generally, a Hermitian matrix (that is, a complex matrix equal to its conjugate transpose) is positive-definite...

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...

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

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...

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...

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

Adjunction formula (algebraic geometry) Adjunction space in topology Conjugate transpose of a matrix in linear algebra Adjugate matrix, related to its inverse...

is the conjugate transpose operator. If B consists entirely of real numbers, which is the case in many applications, the "conjugate transpose" is the...

positive-definite matrix and y † {\displaystyle y^{\dagger }} is the conjugate transpose of y . {\displaystyle y.} For the real case, this corresponds to...