In the Standard Model of particle physics, the Cabibbo–Kobayashi–Maskawa matrix, CKM matrix, quark mixing matrix, or KM matrix is a unitary matrix which contains information on the strength of the flavour-changing weak interaction. Technically, it specifies the mismatch of quantum states of quarks when they propagate freely and when they take part in the weak interactions. It is important in the understanding of CP violation. This matrix was introduced for three generations of quarks by Makoto Kobayashi and Toshihide Maskawa, adding one generation to the matrix previously introduced by Nicola Cabibbo. This matrix is also an extension of the GIM mechanism, which only includes two of the three current families of quarks. The matrix Predecessor – the Cabibbo matrix In 1963, Nicola Cabibbo introduced the Cabibbo angle () to preserve the universality of the weak interaction. Cabibbo was inspired by previous work by Murray Gell-Mann and Maurice Lévy, on the effectively rotated nonstrange and strange vector and axial weak currents, which he references. In light of current concepts (quarks had not yet been proposed), the Cabibbo angle is related to the relative probability that down and strange quarks decay into up quarks ( || and || , respectively). In particle physics jargon, the object that couples to the up quark via charged-current weak interaction is a superposition of down-type quarks, here denoted by . Mathematically this is: or using the Cabibbo angle: Using the currently accepted values for || and || (see below), the Cabibbo angle can be calculated using When the charm quark was discovered in 1974, it was noticed that the down and strange quark could decay into either the up or charm quark, leading to two sets of equations: or using the Cabibbo angle: This can also be written in matrix notation as: or using the Cabibbo angle where the various || represent the probability that the quark of flavor decays into a quark of flavor . This 2×2 rotation matrix is called the "Cabibbo matrix", and was subsequently expanded to the 3×3 CKM matrix. CKM matrix In 1973, observing that CP-violation could not be explained in a four-quark model, Kobayashi and Maskawa generalized the Cabibbo matrix into the Cabibbo–Kobayashi–Maskawa matrix (or CKM matrix) to keep track of the weak decays of three generations of quarks: On the left are the weak interaction doublet partners of down-type quarks, and on the right is the CKM matrix, along