In mathematics, the conjugate transpose (or Hermitian transpose) of an m-by-n matrix A {\\displaystyle {\\boldsymbol {A}}} with complex entries, is the n-by-m matrix obtained from A {\\displaystyle {\\boldsymbol {A}}} by taking the transpose and then taking the complex conjugate of each entry (the complex conjugate of a + i b {\\displaystyle a+ib} being a − i b {\\displaystyle a-ib} , for List of algebra symbols and signs - equivalence, lemniscate, proportional to, factorial, delta, function, e constant, floor, ceiling, absolute value The complex conjugate transpose of a matrix interchanges the row and column index for each element, reflecting the elements across the main diagonal. The operation also negates the imaginary part of any complex numbers. For example, if B = A' and A (1,2) is 1+1i , then the element B (2,1) is 1-1i. Details and Options. 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]]. The complex conjugate transpose of a matrix interchanges the row and column index for each element, reflecting the elements across the main diagonal. The operation also negates the imaginary part of any complex numbers. For example, if B = A' and A(1,2) is 1+1i, then the element B(2,1) is 1-1i. The Conjugate Transpose of a Matrix. We are about to look at an important theorem which will give us a relationship between a matrix that represents the linear Definition. The conjugate transpose of a matrix is the matrix defined by where denotes transposition and the over-line denotes complex conjugation. Remember that the complex conjugate of a matrix is obtained by taking the complex conjugate of each of its entries (see the lecture on complex matrices). In the definition we have used the fact that the order in which transposition and conjugation The symbol \intercal is quite a nice symbol for transpose, but it is placed a little low. Therefore the example defines \transpose to use a \intercal, which is shifted to the baseline. The symbol size adapts to the current math style. The $\dagger$ symbol is often used in quantum mechanics,and also often in general mathematics to represent the conjugate transpose operation.For Hermitian matrices we can write $$A^\dagger=A$$Who Stack Exchange Network Symbol Symbol Name Meaning / definition Example ∠ angle: formed by two rays ∠ABC = 30° measured angle : ABC = 30° spherical angle : AOB = 30° ∟ right angle = 90° α = 90° ° degree: 1 turn = 360° α = 60° deg: degree: 1 turn = 360deg: α = 60deg ′ prime: arcminute, 1° = 60′ α = 60°59′ ″ double prime: arcsecond, 1′ = 60
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