Quaternions and spatial rotation the rotation. As the rotation angles become larger, the slice moves in the negative "z" direction, and the circles become larger until the equator of the sphere is reached, which will correspond to a rotation angle of 180 degrees. Continuing southward, the radii of the circles now become smaller (corresponding to the absolute value of the angle of the rotation considered as a negative number). Finally, as the south pole is reached, the circles shrink once more to the identity rotation, which is also specified as the point at the south pole. Notice that a number of characteristics of such
Zero degrees of freedom concentrates all probability at zero. All of this leaves open the question of what happens with zero degrees of freedom when the noncentrality parameter is not zero. The noncentral chi-squared distribution with zero degrees of freedom and with noncentrality parameter "μ" is the distribution of This concentrates probability "e" at zero; thus it is a mixture of discrete and continuous distributions Zero degrees of freedom In statistics, the non-central chi-squared distribution with zero degrees of freedom can be used in testing the null hypothesis that a sample is from a uniform distribution on the interval (0, 1). This distribution was