A First Course in String Theory
Recall that a group is a set which is closed under an associative multiplication; it contains an identity element, and each element has a multiplicative inverse. Verify that and , as described above, are groups.
What is ?
— Me@2019-05-24 11:25:41 PM
The set of all unitary matrices clearly coincides with the circle group; the unitary condition is equivalent to the condition that its element have absolute value 1. Therefore, the circle group is canonically isomorphic to , the first unitary group.
— Wikipedia on Circle group
In mathematics, a complex square matrix is unitary if its conjugate transpose is also its inverse—that is, if
where is the identity matrix.
In physics, especially in quantum mechanics, the Hermitian conjugate of a matrix is denoted by a dagger () and the equation above becomes
The real analogue of a unitary matrix is an orthogonal matrix. Unitary matrices have significant importance in quantum mechanics because they preserve norms, and thus, probability amplitudes.
— Wikipedia on Unitary matrix
2019.05.25 Saturday ACHK