R can do all kinds of matrix calculations, like multiplication, tranposing and calculating the inverse. The following manual was created by Phil Ender.
Note: R wants the data to be entered by columns starting with column one.
The Matrix
# the matrix function # 1st arg: c(2,3,-2,1,2,2) the values of the elements filling the columns # 2nd arg: 3 the number of rows # 3rd arg: 2 the number of columns > A <- matrix(c(2,3,-2,1,2,2),3,2) > A [,1] [,2] [1,] 2 1 [2,] 3 2 [3,] -2 2
Is Something a Matrix
> is.matrix(A) [1] TRUE > is.vector(A) [1] FALSE
Multiplication by a Scalar
> c <- 3 > c*A [,1] [,2] [1,] 6 3 [2,] 9 6 [3,] -6 6
Matrix Addition & Subtraction
> B <- matrix(c(1,4,-2,1,2,1),3,2) > B [,1] [,2] [1,] 1 1 [2,] 4 2 [3,] -2 1 > C <- A + B > C [,1] [,2] [1,] 3 2 [2,] 7 4 [3,] -4 3 > D <- A - B > D [,1] [,2] [1,] 1 0 [2,] -1 0 [3,] 0 1
Matrix Multiplication
> D <- matrix(c(2,-2,1,2,3,1),2,3) > D [,1] [,2] [,3] [1,] 2 1 3 [2,] -2 2 1 > C <- D %*% A > C [,1] [,2] [1,] 1 10 [2,] 0 4 > C <- A %*% D > C [,1] [,2] [,3] [1,] 2 4 7 [2,] 2 7 11 [3,] -8 2 -4 > D <- matrix(c(2,1,3),1,3) > D [,1] [,2] [,3] [1,] 2 1 3 > C <- D %*% A > C [,1] [,2] [1,] 1 10 > C <- A %*% D Error in A %*% D : non-conformable arguments
Transpose of a Matrix
> AT <- t(A) > AT [,1] [,2] [,3] [1,] 2 3 -2 [2,] 1 2 2 > ATT <- t(AT) >ATT [,1] [,2] [1,] 2 1 [2,] 3 2 [3,] -2 2
Common Vectors
Unit Vector
> U <- matrix(1,3,1) > U [,1] [1,] 1 [2,] 1 [3,] 1
Common Matrices
Unit Matrix
Using Stata
> U <- matrix(1,3,2) > U [,1] [,2] [1,] 1 1 [2,] 1 1 [3,] 1 1
Diagonal Matrix
> S <- matrix(c(2,3,-2,1,2,2,4,2,3),3,3) > S [,1] [,2] [,3] [1,] 2 1 4 [2,] 3 2 2 [3,] -2 2 3 > D <- diag(S) > D [1] 2 2 3 > D <- diag(diag(S)) > D [,1] [,2] [,3] [1,] 2 0 0 [2,] 0 2 0 [3,] 0 0 3
Identity Matrix
> I <- diag(c(1,1,1)) > I [,1] [,2] [,3] [1,] 1 0 0 [2,] 0 1 0 [3,] 0 0 1
Symmetric Matrix
> C <- matrix(c(2,1,5,1,3,4,5,4,-2),3,3) > C [,1] [,2] [,3] [1,] 2 1 5 [2,] 1 3 4 [3,] 5 4 -2 > CT <- t(C) > CT [,1] [,2] [,3] [1,] 2 1 5 [2,] 1 3 4 [3,] 5 4 -2
Inverse of a Matrix
> A <- matrix(c(4,4,-2,2,6,2,2,8,4),3,3) > A [,1] [,2] [,3] [1,] 4 2 2 [2,] 4 6 8 [3,] -2 2 4 > # using MASS package > library(MASS) > AI <- ginv(A) > AI [,1] [,2] [,3] [1,] 1.0 -0.5 0.5 [2,] -4.0 2.5 -3.0 [3,] 2.5 -1.5 2.0 > # using car package > library(car) > AI <- inv(A) > AI [,1] [,2] [,3] [1,] 1.0 -0.5 0.5 [2,] -4.0 2.5 -3.0 [3,] 2.5 -1.5 2.0 > A %*% AI [,1] [,2] [,3] [1,] 1 0 0 [2,] 0 1 0 [3,] 0 0 1 > AI %*% A [,1] [,2] [,3] [1,] 1 0 0 [2,] 0 1 0 [3,] 0 0 1
Inverse & Determinant of a Matrix
> C <- matrix(c(2,1,6,1,3,4,6,4,-2),3,3) > C [,1] [,2] [,3] [1,] 2 1 6 [2,] 1 3 4 [3,] 6 4 -2 > CI <- inv(C) CI [,1] [,2] [,3] [1,] 0.2156863 -0.25490196 0.13725490 [2,] -0.2549020 0.39215686 0.01960784 [3,] 0.1372549 0.01960784 -0.04901961 > d <- det(C) > d [1] -102
Number of Rows & Columns
> X <- matrix(c(3,2,4,3,2,-2,6,1),4,2) > X [,1] [,2] [1,] 3 2 [2,] 2 -2 [3,] 4 6 [4,] 3 1 > dim(X) [1] 4 2 > r <- nrow(X) > r [1] 4 > c <- ncol(X) > c [1] 2
Computing Column & Row Sums
# note the uppercase S > A <- matrix(c(2,3,-2,1,2,2),3,2) > A [,1] [,2] [1,] 2 1 [2,] 3 2 [3,] -2 2 > c <- colSums(A) > c [1] 3 5 > r <- rowSums(A) > r [1] 3 5 0 > a <- sum(A) > a [1] 8
Computing Column & Row Means
# note the uppercase M > cm <- colMeans(A) > cm [1] 1.000000 1.666667 > rm <- rowMeans(A) > rm [1] 1.5 2.5 0.0 > m <- mean(A) > m [1] 1.333333
Horizontal Concatenation
> A > A [,1] [,2] [1,] 2 1 [2,] 3 2 [3,] -2 2 > B <- matrix(c(1,3,2,1,4,2),3,2) > B [,1] [,2] [1,] 1 1 [2,] 3 4 [3,] 2 2 > C <- cbind(A,B) > C [,1] [,2] [,3] [,4] [1,] 2 1 1 1 [2,] 3 2 3 4 [3,] -2 2 2 2
Vertical Concatenation (Appending)
> C <- rbind(A,B) > C [,1] [,2] [1,] 2 1 [2,] 3 2 [3,] -2 2 [4,] 1 1 [5,] 3 4 [6,] 2 2
Rforge 