Frobenious norm
A <- matrix( c( 12, 3, 2, 2, 5, 8, 2, 0, 4 ), nrow=3, ncol=3, byrow=TRUE ) norm(A,"F") frobenius_norm <- function(Mat){ m <- dim(Mat)[1]; n <- dim(Mat)[2]; Sum <- 0; for(i in 1:m){ for(j in 1:n){ Sum = Sum + (abs(A[i,j]))^2; } } return(sqrt(Sum)); } frobenius_norm(A) #same norm(A,"F")