This website is very helpful:
and cor.test is my option of choice
cor.test(x, y,alternative = c("two.sided"),method = c("pearson"))
mat = matrix(rnorm(1000),ncol=10,nrow=100) cor(mat)
'var', 'cov' and 'cor' compute the variance of 'x' and the covariance or correlation of 'x' and 'y' if these are vectors. If 'x' and 'y' are matrices then the covariances (or correlations) between the columns of 'x' and the columns of 'y' are computed.