with a vector of mass eigenstates of down-type quarks. The CKM matrix describes the probability of a transition from one flavour quark to another flavour quark. These transitions are proportional to ||. As of 2020, the best determination of the magnitudes of the CKM matrix elements was: Using those values, one can check the unitarity of the CKM matrix. In particular, we find that the first-row matrix elements give: Although the value seems very nearly 1, its discrepancy is 0.0015; with a standard error of 0.0005, it is 3 standard deviations away from the expected value of 1, in apparent violation of the unitarity condition. This is an interesting hint of physics beyond the Standard Model. The choice of usage of down-type quarks in the definition is a convention, and does not represent a physically preferred asymmetry between up-type and down-type quarks. Other conventions are equally valid: The mass eigenstates , , and of the up-type quarks can equivalently define the matrix in terms of their weak interaction partners , , and . Since the CKM matrix is unitary, its inverse is the same as its conjugate transpose, which the alternate choices use; it appears as the same matrix, in a slightly altered form. General case construction To generalize the matrix, count the number of physically important parameters in this matrix which appear in experiments. If there are generations of quarks (2 flavours) then An × unitary matrix (that is, a matrix such that , where is the conjugate transpose of and is the identity matrix) requires 2 real parameters to be specified. 2 − 1 of these parameters are not physically significant, because one phase can be absorbed into each quark field (both of the mass eigenstates, and of the weak eigenstates), but the matrix is independent of a common phase. Hence, the total number of free variables independent of the choice of the phases of basis vectors is 2 − (2 − 1) = ( − 1)2. Of these, ( − 1) are rotation angles called quark mixing angles. The remaining ( − 1)( − 2) are complex phases, which cause CP violation. = 2 For the case = 2, there is only one parameter, which is a mixing angle between two generations of quarks. Historically, this was the first version of CKM matrix when only two generations were known. It is called the Cabibbo angle after its