correlation between transposon and gene
Ok I think I roughly get what you want to get. Below I simulate something that's like your data because you provided two identical matrices.

#3 TE, 10 tissue, random values
# number of tissue
M1 = matrix(rnorm(30),3,10)
rownames(M1) = paste("TE",1:3,sep="_")
colnames(M1) = paste("Tissue",letters[1:10],sep="_")
## make gene matrix, , random values
M2 = matrix(rnorm(30),3,10)
rownames(M2) = paste("Gene",1:3,sep="_")
colnames(M2) = paste("Tissue",letters[1:10],sep="_")
## here we make TE1 highly correlated to Gene1
M2[1,] = M1[1,] + rnorm(10,0,0.3)
## here we make TE2 highly anti-correlated to Gene2
M2[2,] = -1*M1[2,] + rnorm(10,0,0.3)
#here we calculate for each TE, its correlation with each gene.
#credit to @haci
COR = apply(t(M1),t(M2))
# you can look at the correlation
COR


What you need is the last three rows. Remember, you can only calculate correlation between the gene and the TE, and you do this across all tissue. For example, if gene1 and TE1 has a high correlation, this tells you TE1 expression can predict gene1 expression in most tissue.

It's meaningless to calculate correlation between one data point and another. You need more than 1 value. For example, if you do cor(10,5), it doesn't make sense. 

Hope this is what you are trying to do..