invsigma (mu -mu ) mu reshape ( , invsigma mu reshape ( , mu reshape ( , invsigma @mu reshape ( , xx np linspace - , , yy (-( [ ]xx + )/ [ ][ plt plot(xx ,yy ,' 'plt show ( figure the linear discriminant boundary lies between the two modes of the mixture density and is linear to illustrate the difference between the linear and quadratic casewe specify different covariance matrices for the mixture components in the next example example (quadratic discriminant analysisas in example we consider mixture of two gaussiansbut now with different covariance matrices figure shows the quadratic decision boundary the python code follows figure quadratic decision boundary