General expression of a unitary matrix
Google led me to "http://mathworld.wolfram.com/SpecialUnitaryMatrix.html", where I learned that a "special unitary matrix" U has det(U) = 1 in addition to the "unitary matrix" requirement that U %*% t(Conj(U)) == diag(dim(U)[1]). Thus, if U is a k x k unitary matrix with det(U) = exp(th*1i), exp(-th*1i/k)*U is a special unitary matrix. Moreover, the special unitary matrices are a group under multiplication. Another Google query led me to "http://mathworld.wolfram.com/SpecialUnitaryGroup.html", which gives a general expression for a special unitary matrix, which seems to require three real numbers, not four; with a fourth, you could get a general unitary matrix. spencer graves
J. Liu wrote:
Hi, all, Does anybody got the most general expression of a unitary matrix? I found one in the book, four entries of the matrix are: (cos\theta) exp(j\alpha); -(sin\theta)exp(j(\alpha-\Omega)); (sin\theta)exp(j(\beta+\Omega)); (cos\theta) exp(j\beta); where "j" is for complex. However, since for any two unitary matrices, their product should also be a unitary matrix. When I try to use the above expression to calculate the product, I can not derive the product into the same form. Therefore, I suspect that this may not be the most general expression. Could you help me out of this? Thanks...
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