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Mathematica Stack Exchange is a question and answer site for users of Wolfram Mathematica. It only takes a minute to sign up. Sign up to join this community . Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top Home Questions Tags Users Unanswered How to make the conjugate transpose. Ask Question Asked 4 years, 6 months ago. Active 4 years, 6 months A unitary matrix is a matrix whose inverse equals it conjugate transpose. Unitary matrices are the complex analog of real orthogonal matrices. If U is a square, complex matrix, then the following conditions are equivalent : U is unitary. The conjugate transpose U* of U is unitary. U is invertible and U − 1 = U*. ConjugateTranspose [m] is equivalent to Conjugate [Transpose [m]]. » can be entered as ct or \[ConjugateTranspose]. ConjugateTranspose [m] can also be given as , where can be entered as hc or \[HermitianConjugate]. ConjugateTranspose [m, spec] gives Conjugate [Transpose [m, spec]]. 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 called a self-adjoint matrix or a Hermitian matrix (equivalent to the matrix being equal to its conjugate transpose); that is, A is self-adjoint or Hermitian if \( {\bf A} = {\bf A}^{\ast} . Is there an existing function for the complex conjugate transpose in Mathematica? The equivalent in matlab is the to the apostrophe operator ('). wolfram-mathematica linear-algebra. share | improve this question | follow | edited Dec 13 '11 at 2:42. Mike Bailey. 11.2k 12 12 gold badges 59 59 silver badges 114 114 bronze badges. asked Dec 1 '11 at 4:06. BlueCoffee BlueCoffee. 41 3 3 bronze A conjugate matrix is a matrix A^_ obtained from a given matrix A by taking the complex conjugate of each element of A (Courant and Hilbert 1989, p. 9), i.e., (a_(ij))^_=(a^__(ij)). The notation A^* is sometimes also used, which can lead to confusion since this symbol is also used to denote the conjugate transpose. Using a matrix X in a similarity transformation X^(-1)AX of a given matrix A is also known as conjugating A by X. In this case, B=X^(-1)AX and A are known as similar matrices. Conjugate[z] or z\[Conjugate] gives the complex conjugate of the complex number z. I know that covariance matrix transpose is equal to the matrix itself, but does the same hold for conjugate transpose in case of invertible covariance matrix? linear-algebra covariance. Share. Cite. Improve this question. Follow edited Sep 27 '16 at 14:44. empty bucket. 46 7 7 bronze badges. asked Sep 27 '16 at 12:21. Userhanu Userhanu. 483 3 3 silver badges 10 10 bronze badges $\endgroup Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange Mathematica Stack Exchange is a question and answer site for users of Wolfram Mathematica. It only takes a minute to sign up. Sign up to join this community . Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top Home Questions Tags Users Unanswered How to make conjugate transpose of this matrix? Ask Question Asked 2 months ago. Active 2 months ago
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