[R] questions about discriminant analysis

[ronggui]

i konw the lda and qda in MASS can do discriminant analysis.and lda complete the Fisher's method.and qda is the Quadratic discriminant analysis.
1,my first question is if qda do the Mahalanobis's method?
2,as some textbook say,when using fisher's method,"we proceed by assuming that the within-group covariance structure for our data is the same across groups",so we need test for equailty of covariance matrices. my question is :when i using lda,should i test equailty of covariance matrices first? and can R do these?

thank you !