In a classification problem, in order to choose between LDA and QDA, is it valid to use the correlation matrix instead of the covariance matrix?

Question

I wonder if it is valid to use the Correlation matrix instead of the Covariance matrix to check if a data set is better suited for Linear or for Quadratic Discriminant Analysis. The definitions of these discriminant analysis methods state that the LDA should be used for data with common covariance matrix in each class of the response, while QDA should be used if the covariance matrices are not equal for each class. But plotting the covariance matrix to visually assess this distinction, I thought it would be easier to spot those differences if I use the correlation matrix, for the latter is normalized with the standard deviations for each pair of variable. It is possible or do the division by the standard deviations affect the discriminant analysis premise?